Comparative Analysis of rainfall statistical moments and probability dis-

Next, in order to understand the TPR’s ability to capture the general rainfall regime, key variables and the full statistical rainfall distribution are analysed. The full statistical rainfall distribution is considered to be the combination of a binary occurrence frequency rate with a positive rainfall intensity distribution. Hence, the occurrence frequency, the mean non-zero rainfall intensity as well as the overall mean are assessed over the entire record length for each gauge. Figure 5.10 shows how the agreement between gauges and TPR estimates changes for these key rainfall variables, when relaxing the constraint of only comparing synchronous ob- servations to all available gauge and TPR observations over the same period irrespective of temporal synchronicity. This increases the available data sample for assessment of the TPR, yielding more robust results. Agreement between TPR and gauges for synchronous measure- ments is very weak for the rainfall occurrence frequency as well as for the mean rainfall rate (R2 = 0.34 and R2 = 0.27, respectively), with a slight reduction in the goodness-of-fit when considering all measurements irrespective of temporal synchronicity (R2 = 0.30 andR2 = 0.26, respectively). On the other hand, there is a much stronger linear relationship between TPR and gauge mean rainfall (i.e. the mean of the full rainfall mixed distribution including positive and zero rainfall as shown in fig. 5.10 e &f). Here, the goodness-of-fit improves when considering all measurements (R2 = 0.75) compared to only using synchronous observations (R2 = 0.64). The linear model suggests an under-estimation (negative bias) of gauge rainfall by the TPR of approximately 7% of the respective gauge rainfall rate. Figure 5.11 and fig. 5.12 shows how this relationship varies seasonally with maximum TPR under-estimation of approximately 20% in DJF decreasing to only 6% in SON. However, it should be noted that with the exception of DJF (R2 _{= 0.75), the seasonal relationships are weaker in terms of a lower coefficient of determination}

(R2 ≤0.66) and some extreme outliers, especially in MAM. In terms of the spatial distribution of the correlation coefficient, lower values are found in the Andean regions as opposed to the coastal and continental lowlands (fig. 5.12). A seasonal pattern is observed in the Caribbean

basin where correlation is high during the rain season (summer months) and lower during the dry season (winter months). This behaviour is also evident to a lesser extent in the eastern Colombian Andes.

The general gauge rainfall distribution across the tropical Andes in terms of the cumulative rainfall probability is shown up to the 90th-percentile and above the 90th-percentile in fig. 5.13 and fig. 5.14, respectively. The lowest 40% of the gauge rainfall distribution are constant at 0.6 mm hr-1, which corresponds to the gauge measurement limit, before increasing to 7.2 mm hr-1 at the 90th-percentile. Across the majority of the probability distribution the TPR error is positive, increasing progressively across low rainfall intensities up to a maximum bias of +135% at the 42nd-percentile, before decreasing to +3.5% at the 90th-percentile. Beyond the 90th-percentile TPR under-estimation becomes increasingly negative down to a bias of -37% (absolute error: -11.95 mm hr-1) at the 99th-percentile.

Regional variations in the gauge rainfall distributions in terms of their difference to the average gauge rainfall distribution across the entire Andes are shown in Figure 5.15 (left). While all regions show consistent rates of 0.6 mm hr-1 (i.e. the gauge measurement limit) up to the 40th-percentile, the results show that in the Amazonian and Caribbean lowlands as well as in the central and western Colombian Andes rainfall intensities exceed those of the average gauge rainfall distribution above the 40th_{-percentile with very strong positive deviations above}

the 90th-percentile. Conversely, the Ecuadorian Pacific and Andean regions as well as the eastern Colombian Andes show lower rainfall intensities for the same rainfall probability bins (percentiles). The TPR error (percentage bias) for the individual probability bins (fig. 5.15 right) is not entirely consistent with this pattern. Below the 40th-percentile (highly frequent rainfall) most regions show similar behaviour with continuously increasing bias up to +140- 150% between the 40th and 45th-percentile. In the Ecuadorian Pacific region; however, the bias increases more gradually and peaks later at the 50th-percentile (+100% bias). These results suggest that the quantile-based bias for low rainfall intensities is dependent on the overall rainfall total. Between the 40th and 50th-percentiles the bias drops across all regions and then decreases continuously into a negative bias beyond the 90th-percentile. The outlier here are gauges in the Ecuadorian Andes, which exhibit a similar behaviour of bias reduction but at a far smaller rate, such that at the 90th-percentile there is still a positive bias of +41%, whereas the median bias at the 90th-percentile across all regions is only +3.5%.

Figure 5.9.:a) Match-up plot of synchronous and co-located gauge and TPR rainfall. The red line (X=Y) shows perfect agreement. The blue line shows the average TPR intensity across gauge rainfall intensity bins defined by an exponentially distributed curve. b) - f ) Quantitative precipitation estimation (QPE) statistics by climate region: correlation coefficient, root mean square error (RMSE), mean absolute error (MAE), mean error (ME) and percentage bias, respectively. The boxes extend from the first to the third quartiles (inter-quartile range, IQR), and the whiskers extend to the highest/ lowest value within 1.5 times IQR. The dots represent values outside this range. The values in the top right corner of each plot represent the median performance score across all regions. The numeric identifiers of the regions are ordered as follows: Pacific (1), Amazon (2), Ecuadorian Andes (3), West and Central Colombian Andes (4), Eastern Colombian Andes (5), Caribbean (6).

Figure 5.10.: Scatterplots of TPR and gauge rainfall statistical variables based only on syn- chronous and co-located measurements (right panel) and all gauge and TPR mea- surements over the observational period (left panel): a) - b)occurrence frequency,

c) - d)mean rainfall intensity (mm hr-1), e) - f )mean of the full rainfall distri- bution (zero rainfall and positive rainfall intensities). The black line shows perfect agreement (X=Y) and the green line the optimal linear model printed in the graph.

Figure 5.11.: Same as Figure 5.10 but for the mean of the full rainfall distribution across different seasons.

Figure 5.12.: Histograms of correlation of mean monthly rainfall between TPR and daily gauges across distinct regions in Colombia. Printed value represents correlation between mean annual TPR and daily gauges in respective region.

Figure 5.13.: Inverted cumulative frequency distributions (CDFs) showing the cumulative prob- ability (F(x) on the x-axis and on the y-axis the variation in gauge rainfall intensity across the 78 stations for each quantile bin up to the 0.9 quantile (top panel), the variation in the absolute difference between corresponding TPR and gauge quan- tiles (middle panel) and the variation in the relative error between corresponding TPR and gauge quantiles (bottom panel). The red lines indicate no error, while the dashed red line indicates an error magnitude equal to gauge rainfall intensity. The boxes extend from the first to the third quartiles (inter-quartile range, IQR), and the whiskers extend to the highest/ lowest value within 1.5 times IQR.

Figure 5.14.: Same as fig. 5.13 but for F(x)>0.9.

Figure 5.15.: Cumulative distribution frequencies (CDFs) of gauge rainfall intensities for all regions (left) and the corresponding TPR bias in percentage, relative to the mag- nitude of the gauge rainfall intensity for that quantile (right).