# The Summertime Diurnal Cycle of Precipitation Derived from IMERG
## 3 Results
### Case Studies of the Diurnal Cycle of Precipitation  
Two case studies are presented to show how the harmonic function is fitted to the IMERG-derived precipitation occurrence, intensity and accumulation. A land-based region over Cambodia and Vietnam, and an oceanic region adjacent to the eastern coast of the US (specifically the states of North and South Carolina) are selected due to their tendency to experience rainfall with a noticeable diurnal variation.  
Figure 1 depicts the summertime diurnal cycle of precipitation occurrence, intensity and accumulation for Cambodia and Vietnam. Occurrence and accumulation are clearly dominated by the 24h harmonic (green line), which has a larger amplitude (\(A_{1}/f_{0}=63.4\%\pm 7.2\%\) and 85.9% \(\pm\) 4.4%, respectively) in comparison with the 12 h harmonic (blue line, \(A_{2}/f_{0}=9.8\%\pm 7.2\%\) and 29.9% \(\pm\) 4.5%, respectively). Both occurrence and accumulation peak in the evening, with \(T_{1}=20.0\) LST \(\pm\) 0.4 LST and 20.3 LST \(\pm\) 0.2 LST, respectively. Intensity appears to be evenly contributed to by the 24 h and 12 h harmonics (\(A_{1}/f_{0}=30.4\%\pm 11.1\%\), \(A_{2}/f_{0}=33.6\%\pm 11.2\%\)), with the 24 h trough and first 12 h peak superimposing to produce an initial muted diurnal peak at \(\sim\)6 LST, whilst the 24 h peak and second 12 h peak superimpose to produce a larger second diurnal peak at \(\sim\)19 LST. The harmonic function appears to better represent precipitation accumulation (\(R^{2}=0.98\), \(V_{F(t)}/V_{d}=89.9\%\)) compared to occurrence and intensity (\(R^{2}=0.88\) and 0.73, \(V_{F(t)}/V_{d}=88.3\%\) and 64.1%, respectively), as evidenced by the smaller deviations in data (black circles) from the harmonic function (red line) and the smaller 95% confidence intervals on the function (red shading). This trend is true for most of the globe, with the harmonic function better fitting to accumulation than to occurrence and intensity (i.e., highest \(R^{2}\)) for 81.4% of land and ocean quality-controlled grid boxes.  
Figure 2 depicts the summertime diurnal cycle of precipitation occurrence, intensity and accumulation for the Atlantic Ocean near the coast of North and South Carolina, US. Occurrence, intensity and accumulation are all dominated by the 24 h harmonic (\(A_{1}/f_{0}=42.8\%\pm 6.9\%\), 33.7% \(\pm\) 11.2% and 66.3% \(\pm\) 2.9%, respectively) as opposed to the 12h harmonic (\(A_{2}/f_{0}=10.2\%\pm 6.9\%\), 6.3% \(\pm\) 9.0% and 3.4% \(\pm\) 2.9%, respectively), with the diurnal cycle peaking in the morning at \(\sim\)12 LST, 7 LST and 10 LST, respectively. As for the land-based case study, the harmonic function best represents accumulation, followed by occurrence and worst represents intensity (\(R^{2}=0.98\), 0.79 and 0.52, \(V_{F(t)}/V_{d}=97.3\%\), 79.5% and 52.0%, respectively). Notably for both land and ocean case studies, the amplitude and phase of the 24 h and 12 h harmonics representing the diurnal cycle of intensity should be treated with caution due to the poor fitting of the harmonic function. Clearly the use of only 24 h and 12 h harmonics is not sufficient for capturing the diurnal cycle.