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FIG. 7. (a) Fractional distribution of the event-based contingency table for WCRs, SCRs, and MCSs. True false alarms are excluded since only time steps associated with rainfall types are considered. (b) Q-Q plots of rain rates for time steps with hits for WCRs, SCRs, and MCSs.

Figure 7 (a) Fractional distribution of the event-based contingency table for WCRs, SCRs, and MCSs. True false alarms are excluded since only time steps associated with rainfall types are considered. (b) Q-Q plots of rain rates for time steps with hits for WCRs, SCRs, and MCSs.

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Fic. 1. Distribution of the DACCIWA RG stations in the Ashanti region of Ghana (see mar inset in the upper-left corner). Each red number represents an RG with names given in the top- right inset. The blue grid illustrates the IMERG pixels. RG-associated IMERG pixels that are used for the point-to-pixel comparison are denoted by the light-red shading. The gray shaded background shows the topography of the study region as provided by the Global Land One-km Base Elevation Project (GLOBE; Hastings et al. 1999).
Fic. 1. Distribution of the DACCIWA RG stations in the Ashanti region of Ghana (see mar inset in the upper-left corner). Each red number represents an RG with names given in the top- right inset. The blue grid illustrates the IMERG pixels. RG-associated IMERG pixels that are used for the point-to-pixel comparison are denoted by the light-red shading. The gray shaded background shows the topography of the study region as provided by the Global Land One-km Base Elevation Project (GLOBE; Hastings et al. 1999).
Fic. 2. Schematic showing how hits, misses, and false alarms are defined based on an exemplary half-hourly rainfall pattern in (first row) RG and (second row) IMERG with wet (black, =0.2mmh_') and dry time steps (white). (third row) The standard approach designates misses (false alarms) wherever a rainy time step in RG (IMERG) is associated with a dry time step in IMERG (RG). (fourth row) In the event-based approach, misses (false alarms) in adjacent time steps of hits are considered as a reduction (prolongation) of the event duration, hence termed Duration— (Duration+). ‘Isolated’ errors are called true misses and false alarms, respectively.
Fic. 2. Schematic showing how hits, misses, and false alarms are defined based on an exemplary half-hourly rainfall pattern in (first row) RG and (second row) IMERG with wet (black, =0.2mmh_') and dry time steps (white). (third row) The standard approach designates misses (false alarms) wherever a rainy time step in RG (IMERG) is associated with a dry time step in IMERG (RG). (fourth row) In the event-based approach, misses (false alarms) in adjacent time steps of hits are considered as a reduction (prolongation) of the event duration, hence termed Duration— (Duration+). ‘Isolated’ errors are called true misses and false alarms, respectively.
FIG. 3. (a) Scatterplot showing the duration and mean rainfall rate (i.e., integrated rainfall amount divided by the duration) of all individual rainfall events within the study period 2016-17. Different colors denote the rainfall types listed in the legend and as characterized by Dezfuli et al. (2017b). Here, %n and %RR designate the relative frequency and fractional rainfall contribution, respectively, both in %. (b)—(d) Marker plots showing composites of rainfall rates in 5-min bins against elapsed time of event for weak convective rainfall (WCR), strong convective rainfall (SCR), and mesoscale convective systems (MCSs), respectively. The bin median values are denoted by connected circles, whereas the interquartile range is given by the colored bars. The median for each bin is calculated by all available events, the number of which decreases toward longer durations (not shown). The green curve is the cumulative median rainfall.
FIG. 3. (a) Scatterplot showing the duration and mean rainfall rate (i.e., integrated rainfall amount divided by the duration) of all individual rainfall events within the study period 2016-17. Different colors denote the rainfall types listed in the legend and as characterized by Dezfuli et al. (2017b). Here, %n and %RR designate the relative frequency and fractional rainfall contribution, respectively, both in %. (b)—(d) Marker plots showing composites of rainfall rates in 5-min bins against elapsed time of event for weak convective rainfall (WCR), strong convective rainfall (SCR), and mesoscale convective systems (MCSs), respectively. The bin median values are denoted by connected circles, whereas the interquartile range is given by the colored bars. The median for each bin is calculated by all available events, the number of which decreases toward longer durations (not shown). The green curve is the cumulative median rainfall.
TABLE 1. Performance evaluation of IMERG based on the measures introduced in section 3 for different categories, namely, all available time steps (section A), rain rate intervals (section B), rainfall types (section C), and seasons (section D). Note again that only hits are considered for calculation of the rain rate error measures ME, MAE, NME, and NMAE. In section B, rain rates are based on the RGs. Therefore, false alarms and correct negatives are not quantified. In section C, rainy time steps in the RGs and IMERG not associated with the respective rainfall type, i.e., all true false alarms and rainfall of the other rainfall types, are set to zero. Thus, misses include both true misses and Duration—, whereas false alarms contain only Duration+. The dependence of IMERG’s performance on certain rain rate intervals observed by the RGs is evaluated in section B of Table 1. Here, only POD can be quantified out of the contingency measures. Increasing rain rates as measured by the RGs are associated with an increase in POD. However, the rain rate intervals are differently biased. As seen in ME, the positive bias at low RG in- tensities turns strongly negative at high rain rates. nterestingly, for the weakest and most intense intervals, the absolute value of ME is nearly the same as MAE. Hence, at simultaneous RG and IMERG time steps, ow- and high-intensity RG values are almost exclu- sively over and underestimated, respectively. IMERG time steps. The scatterplot in Fig. 6a illustrates how the half-hourly rain rate pairs are distributed. Note that only hits are considered here. The bulk of data points comprise rainfall rates in the range of 1-10mmh ' and is located close to the 1:1 line. However, the overall variability is high, suggesting is- sues in rain rate estimation and/or timing. The latter was found to affect the skill of PMW retrievals (You et al. 2019, see section 8 for a brief discussion). The regression line, determined with the error model in Tian et al. (2013), further indicates a positive and negative bias for low and high rain rates, respectively. Ignoring corresponding time steps and arranging this data subset in a quantile—quantile (Q—Q) plot, differ- ences in the underlying distribution of rainfall rates between the RGs and IMERG as well as biases can be made visible in a more comprehensive manner (Fig. 6b). While rain rates are almost evenly distrib- uted up to 2mmh |, the negative bias in IMERG at higher rain rates becomes increasingly evident. Overall, IMERG is unable to resolve the most extreme rainfall rates. Expressed as cumulative distributions, rainfall rates for hits and other elements from the event-based contingency table are compared in Fig. 6c. Around 70% of time steps containing true false alarms are equal or less than 1mmh ' with a median of 0.55mmh | (short vertical orange line at the bottom). This is also true for roughly 50% of all Duration+ time steps. This hints toward a generally flawed formulation for very low-intensity rainfall in IMERG. At the same time, the subsets of true misses as well as Duration— comprise markedly higher rain rates.
TABLE 1. Performance evaluation of IMERG based on the measures introduced in section 3 for different categories, namely, all available time steps (section A), rain rate intervals (section B), rainfall types (section C), and seasons (section D). Note again that only hits are considered for calculation of the rain rate error measures ME, MAE, NME, and NMAE. In section B, rain rates are based on the RGs. Therefore, false alarms and correct negatives are not quantified. In section C, rainy time steps in the RGs and IMERG not associated with the respective rainfall type, i.e., all true false alarms and rainfall of the other rainfall types, are set to zero. Thus, misses include both true misses and Duration—, whereas false alarms contain only Duration+. The dependence of IMERG’s performance on certain rain rate intervals observed by the RGs is evaluated in section B of Table 1. Here, only POD can be quantified out of the contingency measures. Increasing rain rates as measured by the RGs are associated with an increase in POD. However, the rain rate intervals are differently biased. As seen in ME, the positive bias at low RG in- tensities turns strongly negative at high rain rates. nterestingly, for the weakest and most intense intervals, the absolute value of ME is nearly the same as MAE. Hence, at simultaneous RG and IMERG time steps, ow- and high-intensity RG values are almost exclu- sively over and underestimated, respectively. IMERG time steps. The scatterplot in Fig. 6a illustrates how the half-hourly rain rate pairs are distributed. Note that only hits are considered here. The bulk of data points comprise rainfall rates in the range of 1-10mmh ' and is located close to the 1:1 line. However, the overall variability is high, suggesting is- sues in rain rate estimation and/or timing. The latter was found to affect the skill of PMW retrievals (You et al. 2019, see section 8 for a brief discussion). The regression line, determined with the error model in Tian et al. (2013), further indicates a positive and negative bias for low and high rain rates, respectively. Ignoring corresponding time steps and arranging this data subset in a quantile—quantile (Q—Q) plot, differ- ences in the underlying distribution of rainfall rates between the RGs and IMERG as well as biases can be made visible in a more comprehensive manner (Fig. 6b). While rain rates are almost evenly distrib- uted up to 2mmh |, the negative bias in IMERG at higher rain rates becomes increasingly evident. Overall, IMERG is unable to resolve the most extreme rainfall rates. Expressed as cumulative distributions, rainfall rates for hits and other elements from the event-based contingency table are compared in Fig. 6c. Around 70% of time steps containing true false alarms are equal or less than 1mmh ' with a median of 0.55mmh | (short vertical orange line at the bottom). This is also true for roughly 50% of all Duration+ time steps. This hints toward a generally flawed formulation for very low-intensity rainfall in IMERG. At the same time, the subsets of true misses as well as Duration— comprise markedly higher rain rates.
FIG. 6. Comparison of rain rates between the RGs and IMERG. (a) Scatterplot with RG rain rates on the x axis and IMERG rain rates on the y axis. Only hits are considered. Darker colors indicate a higher density of points. The regression line was calculated using the multiplicative error model of Tian et al. (2013). The parameters on the bottom right are total number of hits n, the y intersect a, slope B, and standard deviation o of the regression in the natural logarithm space of the error model, and the p value of the regression. (b) Quantile—quantile (Q—Q) plot of RG (x axis) and IMERG (jy axis) rain rates. The positions of the 10th, 50th, and 90th percentiles are highlighted. (c) Cumulative rain rate distribution of the event-based contingency table (Fig. 2). The distribution of the RG rain rates are plotted in black as a reference. The colored lines at the bottom denote the respective median values.
FIG. 6. Comparison of rain rates between the RGs and IMERG. (a) Scatterplot with RG rain rates on the x axis and IMERG rain rates on the y axis. Only hits are considered. Darker colors indicate a higher density of points. The regression line was calculated using the multiplicative error model of Tian et al. (2013). The parameters on the bottom right are total number of hits n, the y intersect a, slope B, and standard deviation o of the regression in the natural logarithm space of the error model, and the p value of the regression. (b) Quantile—quantile (Q—Q) plot of RG (x axis) and IMERG (jy axis) rain rates. The positions of the 10th, 50th, and 90th percentiles are highlighted. (c) Cumulative rain rate distribution of the event-based contingency table (Fig. 2). The distribution of the RG rain rates are plotted in black as a reference. The colored lines at the bottom denote the respective median values.
Fic. 8. Comparison between RG and IMERG with respect to total rainfall and representation of rainfall types using the event- based approach of the contingency table (Fig. 2), all averaged over collocated RGs and IMERG pixels. (a) Monthly integrated rainfall difference for rainfall types. (b) As in Fig. 4b, but for IMERG. The fractional rainfall contribution of true false alarms is denoted as orange bars. The solid and dashed white curves are identical to the black curve and gray area, respectively, in Fig. 4c. (c) As in (b), but for true misses. The left axis refers to the white curve and the right axis to the stacked bars.
Fic. 8. Comparison between RG and IMERG with respect to total rainfall and representation of rainfall types using the event- based approach of the contingency table (Fig. 2), all averaged over collocated RGs and IMERG pixels. (a) Monthly integrated rainfall difference for rainfall types. (b) As in Fig. 4b, but for IMERG. The fractional rainfall contribution of true false alarms is denoted as orange bars. The solid and dashed white curves are identical to the black curve and gray area, respectively, in Fig. 4c. (c) As in (b), but for true misses. The left axis refers to the white curve and the right axis to the stacked bars.
FIG. 10. (a) Standard approach of the contingency table based on all available time steps in the IMERG sources. The absolute numbers of time steps as well as their fraction relative to all IMERG time steps are given on the right axis. Note that the axis is truncated at 10% for more clarity. The fraction of correct negatives extends further to 100%. (b) Q—Q plot of RG rain rates (x axis) and those of the IMERG sources (y axis). The respective positions of the 10th, 50th, and 90th percentiles are highlighted.
FIG. 10. (a) Standard approach of the contingency table based on all available time steps in the IMERG sources. The absolute numbers of time steps as well as their fraction relative to all IMERG time steps are given on the right axis. Note that the axis is truncated at 10% for more clarity. The fraction of correct negatives extends further to 100%. (b) Q—Q plot of RG rain rates (x axis) and those of the IMERG sources (y axis). The respective positions of the 10th, 50th, and 90th percentiles are highlighted.
Fic. 12. As in Fig. 9, but based on the IMERG sources. Figure 13 compares the probability distribution of cloud-top properties described in section 2 around all rainy time steps within the different sources (colored lines) with those of the RGs (gray shade). Here, we distinguish between cloud tops in ice (Figs. 13a—d) and liquid phases (Figs. 13e—-h), the latter of which is associated with warm rain. Note again that the sample consists of daytime rainfall only since the retrieval of COT and Reg requires sunlight as input (see section 2). Although available at all times, the
Fic. 12. As in Fig. 9, but based on the IMERG sources. Figure 13 compares the probability distribution of cloud-top properties described in section 2 around all rainy time steps within the different sources (colored lines) with those of the RGs (gray shade). Here, we distinguish between cloud tops in ice (Figs. 13a—d) and liquid phases (Figs. 13e—-h), the latter of which is associated with warm rain. Note again that the sample consists of daytime rainfall only since the retrieval of COT and Reg requires sunlight as input (see section 2). Although available at all times, the
Fic. 13. Probability distributions of cloud properties described in section 2 based on all rainy time steps in the RGs (gray shaded), IMERG, and its sources (colored lines), separated into (a)—(d) glaciated cloud tops and (e)—(h) warm/liquid cloud tops. Note the different scales for CTT between glaciated and liquid cloud tops. The colored vertical lines at the bottom of each plot denote the median values of the respective distribution.
Fic. 13. Probability distributions of cloud properties described in section 2 based on all rainy time steps in the RGs (gray shaded), IMERG, and its sources (colored lines), separated into (a)—(d) glaciated cloud tops and (e)—(h) warm/liquid cloud tops. Note the different scales for CTT between glaciated and liquid cloud tops. The colored vertical lines at the bottom of each plot denote the median values of the respective distribution.
TABLE 2. As in Table 1, but for glaciated cloud tops (section A) and warm/liquid cloud tops (section B), and further decomposed into IMERG and its sources. by CTT, where pronounced differences between the RGs and hits are apparent as well (Fig. 14h). Overall, this is the reason for frequent misses of WCR events during the little dry season, which are predominantly produced by warm clouds (not shown). At the same time, the aforementioned overestimation of rain occur- rences for CTTs around 260 K are typically false alarms. oversensitivity toward low IWP values (orange), which can be traced back to a flawed relationship with COT (Fig. 14b). In contrast, the high similarity between the contingency elements and RGs with respect to Reger, in- dicates that hits, false alarms and misses can hardly be predicted with Re ;. Considering CTT, the distribution of misses is shifted towards higher values compared to that of the RG observation (Fig. 14d), that is, clouds at lower altitudes.
TABLE 2. As in Table 1, but for glaciated cloud tops (section A) and warm/liquid cloud tops (section B), and further decomposed into IMERG and its sources. by CTT, where pronounced differences between the RGs and hits are apparent as well (Fig. 14h). Overall, this is the reason for frequent misses of WCR events during the little dry season, which are predominantly produced by warm clouds (not shown). At the same time, the aforementioned overestimation of rain occur- rences for CTTs around 260 K are typically false alarms. oversensitivity toward low IWP values (orange), which can be traced back to a flawed relationship with COT (Fig. 14b). In contrast, the high similarity between the contingency elements and RGs with respect to Reger, in- dicates that hits, false alarms and misses can hardly be predicted with Re ;. Considering CTT, the distribution of misses is shifted towards higher values compared to that of the RG observation (Fig. 14d), that is, clouds at lower altitudes.
Fic. 14. As in Fig. 13, but for the elements of the standard contingency table. Results are shown for IMERG only As mentioned in section 2, all results presented in this study must first be understood from the perspective of a point-to-pixel validation. While IMERG contains area-averaged rainfall information within its 0.1° grid (Huffman et al. 2019c), almost every pixel is compared with only a single RG. This discrepancy in spatial rep- resentativeness may affect some of the error measures
Fic. 14. As in Fig. 13, but for the elements of the standard contingency table. Results are shown for IMERG only As mentioned in section 2, all results presented in this study must first be understood from the perspective of a point-to-pixel validation. While IMERG contains area-averaged rainfall information within its 0.1° grid (Huffman et al. 2019c), almost every pixel is compared with only a single RG. This discrepancy in spatial rep- resentativeness may affect some of the error measures
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