3.1. Rainfall Disaggregation
As mentioned earlier, this study used two cases to disaggregate rainfall data from a daily to an hourly timescale. For case 1, the NPRED-MoF algorithm was adopted, in which the temperature variable as well as the rainfall variable was used for the disaggregation. For case 2, the conventional KNN method was used to disaggregate the rainfall by using the rainfall variable alone (i.e., without temperature). The effect of the two methods on the disaggregation of rainfall data from a daily to an hourly timescale is discussed below for three examples of the future climate, each of which used a different RCM ensemble member.
The first example was a climate ensemble member for the year 2074 and a daily rainfall value of 49.91 mm. When this daily rainfall value was disaggregated to an hourly scale by using the two cases of rainfall disaggregation, case 1 gave a rainfall temporal pattern with a peak of 25.1 mm and case 2 gave a temporal pattern with a peak of 13.6 mm. (It is worth noting that the peaks in this example and the rest of the examples in this section were the AM values for the duration of 1 h since the concentration time was found to be 1 h). Hence it was clear that the difference between the two peaks (i.e., the AMs) of the hourly disaggregated data produced by the two cases of disaggregation for this future climate example was considerable and would also lead to big differences in the derived IDF curves.
In the second RCM ensemble example, in contrast to the previous example where the peak of rainfall temporal pattern for the disaggregated data produced by case 1 was lower than that produced by case 2. Such disaggregation was for a future daily rainfall value of 105.3 mm and the year 2094 that gave peaks (which are the same as the AMs) of 28 mm and 45.3 mm when subjected to case 1 and case 2 disaggregation, respectively.
Interestingly, in the third RCM ensemble example, cases 1 and 2 produced the same rainfall temporal pattern, and consequently, the same peaks and AMs for the disaggregated data for the year 2084, as well as a daily rainfall value of 58 mm that gave a peak of 12.88 mm.
It is clear from the above examples that the differences in the AM values that resulted from the two cases of disaggregation were significant. It is also logical to conclude that such differences would highly affect the derived IDF curves for the current and future climates and consequently produce high uncertainty. Furthermore, this uncertainty resulted not just from the disaggregation method, but from the number of climate variables that were used for the disaggregation.
In order to make it easier for the reader to visualize the difference in AMs between the two cases of rainfall disaggregation, Figure 2
a,b shows an example of the AM values for the disaggregated daily rainfall and for the current and future climates with a duration of 1 h. The future modeled rainfall data in Figure 2
b and the above three examples were bias corrected based on the last reference period.
3.2. IDF Curves
The IDF curves for the current and future climates were derived for a small urban area in West Yorkshire by using the following: 11 RCM ensemble members, 5 rainfall durations, 6 return periods, 8 reference periods to bias correct the RCM, and 2 cases for rainfall disaggregation using the rainfall variable with and without the temperature variable. Then, the IDF curves were used to determine the percentage of relative change between the current and future climate. In addition, the uncertainty (which is the range of the results) of the future climate outputs was investigated by comparing 16 sets of future IDF curves. These sets were derived based on two cases of rainfall disaggregation and on the eight reference periods that were adopted to bias correct the future RCM rainfall data.
An example of the difference in IDF curves for both the current and future climate is presented in Figure 3
for the first and last reference periods and the two cases of rainfall disaggregation. The plots in the figure show that the future IDF curves differ from those of the current climate and the extent of the difference between them arises from the reference period (as previously stated by Fadhel et al. [38
]), and also from the rainfall disaggregation method (i.e., the use or otherwise of the temperature variable together with the historical rainfall). In this study, the focus is not on the uncertainty that results from the reference period because this issue has already been addressed by Fathel et al. [38
]. Instead, this study is interested in the uncertainty that may result from the rainfall disaggregation, where again this does not mean the uncertainty that results from the type of disaggregation method, but rather from the number of climate variables that are used for the disaggregation.
It is clear from Figure 3
(and Figures S1–S5 in the Supplementary Material
and from the rest of the figures for the reference periods and rainfall disaggregation cases that are not shown here) that the projected rainfall intensity for most of the RCM ensemble members tends to increase for all frequencies, durations, reference periods, and rainfall disaggregation when case 2 is applied (i.e., without using the temperature variable). However, the results for future rainfall intensity, when also including the temperature variable in the rainfall disaggregation procedure (i.e., case 1), are similar to those of case 2 for all frequencies and durations except the first duration (i.e., 1 h) where the first five reference periods tend to project a decrease in the future rainfall intensity starting from the second return period (i.e., 5 years). Such a decrease in the projected rainfall intensity for the first duration is later shown by all the reference periods for the last three return periods (i.e., 25, 50, and 100 years) and by most of the climate ensemble members.
An interesting finding in respect of the results for the derived IDF curves was that the rainfall intensity for both the current and future climate which resulted from applying case 1 rainfall disaggregation (i.e., with temperature) was higher than that produced by case 2. This difference was seen for all reference periods, frequencies, and durations. As stated earlier in the Introduction, Wasko and Sharma [44
] and Fadhel et al. [45
] showed that in addition to the scaling of rainfall volume with temperature, each segment of the rainfall temporal pattern scales differently with temperature, especially the peak segment which scales positively with temperature. Consequently, the rainfall temporal pattern for the disaggregated rainfall based on the temperature and rainfall variables highly differs from that based on the rainfall variable alone, especially for the future climate scenarios because the weather is becoming warmer. Thus, disaggregating the rainfall based on case 2 (i.e., without temperature) can lead to a high over-under estimation of the actual results and uncertain outputs in regard to the derived IDF curves for both the current and future climate. It is also worth mentioning that the maximum likelihood estimate method was adopted to check the significance of the results at the 95% level and was applied to the parameters used for deriving the IDF curves (results not shown).
In this study, for each of the two cases of rainfall disaggregation, the percentage change between the future and current climate for the mean of the 11 RCM ensemble members was found in order to investigate the difference between the two climates and then compare the results of the two cases of rainfall disaggregation. A sample of the results is shown in Table 1
for 5 rainfall durations, the 2 cases of rainfall disaggregation, 8 reference periods, and the 10-year return period.
It is clear from Table 1
and the rest of the unshown results that by adopting the temperature variable to disaggregate the rainfall, the percentage change between the two climates was lower than the corresponding values for the case of disaggregation based on only the rainfall variable even though the rainfall values for both the current and future climates generated by the case 1 disaggregation method were higher than those obtained by applying case 2. This was true for all reference periods, durations, and frequencies with a few exceptions, vice versa. Such exceptions included (a) the first return period (2 years) for the first duration (1 h) and the last three reference periods; (b) the first return period for the second to the fourth durations (3 to 12 h) and all reference periods, and (c) the third duration (6 h) for all return periods and the last reference period.
However, the percentage change between the future and current climate for case 1 disaggregation and the first duration (i.e., 1 h) tended to indicate a projected decrease in the future rainfall intensity compared to the current climate for all return periods except for the first return period. Such a decrease in the projected rainfall intensity for the first duration was shown by five reference periods for the second return period (i.e., 5 years), and later expanded to include all eight reference periods for the last three return periods (i.e., 25, 50 and 100).
On the other hand, for the third return period (i.e., 10 years), only the seventh reference period showed a slight increase in future rainfall intensity compared to the current climate with a value of 0.64%, as shown in Table 1
. By comparing the percentage change (i.e., for the seventh reference period, 1 h duration, and 10-year return period) by case 1 with that of case 2, it can be seen that the percentage change by case 1 was much lower than that by case 2 (i.e., 0.64% vs. 22.4%). Thus, the difference between the two values of percentage change for the two cases of rainfall disaggregation was 21.8%.
Staying with the same duration and return period (i.e., 1 h, 10 years) for case 1 rainfall disaggregation, the first reference period showed the maximum decrease in terms of the percentage change between the two climates with a value of −14.7%. However, the corresponding value for case 2 rainfall disaggregation in the first reference period showed an increase of 14.6%. Hence the difference between the predictions of the two cases is 29.3%. As can be seen from Table 1
(and the unshown results), the difference in the percentage change value between the two cases of disaggregation was higher for shorter durations and decreased as the duration increased for each return period.
As such differences in the percentage change values between the two cases of rainfall disaggregation were large compared with the return period and rainfall duration, the effect of the return period and rainfall duration on the percentage change between the current and future climate over the eight reference periods was investigated further for each case of rainfall disaggregation. Hence, the uncertainty in the difference between the results produced by the two cases of disaggregation were inspected as well.
It was found that the results (i.e., uncertainty in the difference in the percentage change between the two cases of rainfall disaggregation) varied over the eight reference periods. For each rainfall duration, the uncertainty of the results tended to increase as the return period increased. However, for each return period, the uncertainty in the difference of the projections between the two cases of rainfall disaggregation reduced as the rainfall duration increased over the eight reference periods. This was observed for all return periods except the first one (2 years) where the uncertainty declined for the first two durations (1 and 3 h) and increases for the last three (6, 12, and 24 h).
Since the projection results based on the two cases of rainfall disaggregation were not consistent for shorter durations and longer return periods, the results for all durations and return periods were examined in more detail. Figure 4
and Figure 5
show an example of the analysis of a short and a long duration of 3 h and 12 h, respectively, where both the current and future climates were plotted for the 8 reference periods, different return periods, the mean of the 11 RCM ensemble members, and the 2 cases of rainfall disaggregation.
It is clear from the graphs in Figure 4
a,b and for a duration of 3 h, that for a specific rainfall intensity under the current climate that happened once every 50 years, the probability of such a specific rainfall occurring in any year was p
= 2%. For the same rainfall intensity, but under future climate conditions and for case 1 rainfall disaggregation, the return period was found to vary between 21.2 and 40.7 years (i.e., p
= 4.7–2.5%) based on the eight reference periods (Figure 4
a). However, for case 2 rainfall disaggregation, the return period was found to be earlier than that for case 1 and it varied between 10.2 and 16.4 years (i.e., p
= 9.8–6.1%) (Figure 4
b). This means that the difference between the two ranges of the return period for the future climate depending on the two cases of rainfall disaggregation was between 11 and 24.3 years. When the above analysis was repeated for the duration of 12 h, it was noticed that the uncertainty varied between 17.8 and 30 years (Figure 5
a) and between 9.9 and 16.9 years (Figure 5
b) for case 1 and case 2, respectively. Thus, the difference between the two ranges for the two cases of disaggregation varied between 7.9 and 13.1 years. The above results were significant at the 95% level and are shown in a table within Figure 4
and Figure 5
It is clear from the above analysis (and the unshown results) that the extent of uncertainty regarding a specific rainfall intensity under the current climate that is expected to appear in the future but with a shorter return period varies according to the case of disaggregation over the reference periods. In other words, the extent of uncertainty varies according to the climate variables that are used as predictors for the disaggregation. Such uncertainty is higher when the historical temperature and rainfall variables are adopted as predictors to disaggregate the rainfall as compared to using only the rainfall variable for disaggregation, and moreover, the uncertainty is significant for shorter durations and longer return periods. In addition, the difference between the results of the two cases of rainfall disaggregation is considerable for short durations and longer return periods.
Usually, global climate models and RCMs employ ensemble members to mitigate the uncertainty of future climate projections. The remainder of this section focuses on the uncertainty of future rainfall projections for 3 out of the 11 climate ensemble members: (1) the driest ensemble member; (2) the wettest ensemble member, and (3) the mean of the 11 RCM ensemble members. Table 2
presents a sample of the results of the projected rainfall intensity for future climate for the 10-year return period, 5 rainfall durations, 8 reference periods, and the 2 cases of rainfall disaggregation for the driest ensemble member, wettest ensemble member, and the mean of the 11 RCM ensemble members.
The wettest ensemble member is also known as the “pessimistic” climate scenario [11
] since it gives the highest projection compared to the other climate ensemble members. In this study, it was found that the uncertainty related to the difference between the projected results based on the two cases of rainfall disaggregation and for all the reference periods increased as the return period increased for a specific rainfall duration. This uncertainty was considerable for small rainfall durations, especially the first two durations, but it tended to become less pronounced for rainfall durations higher than 6 h as the return period increased. However, the uncertainty of the future rainfall intensity that resulted from the difference between the two cases used to disaggregate the rainfall tended to decrease as the rainfall duration lengthened for a specific return period.
Similarly, the uncertainty for the driest ensemble member and the mean of the 11 RCM ensemble members increased for short rainfall durations and long return periods. Nevertheless, the extent of uncertainty was much lower than that for the wettest ensemble member.
As mentioned earlier, and as seen from Table 2
as well as the unshown results, the rainfall projections based on disaggregation by using both the temperature and the rainfall variables (case 1) were higher than the corresponding projections based on disaggregation by the rainfall variable alone (case 2). This was true for all reference periods, frequencies, and durations except for the last duration (24 h). For the 24 h duration, only the projections for a few climate ensemble members based on case 1 rainfall disaggregation were lower than the corresponding results based on case 2 rainfall disaggregation. However, the difference between these results for the two cases were very small because the predictions of the future rainfall intensity based on the two cases of rainfall disaggregation tended to be close to each other for the long durations and especially for the longest duration (i.e., 24 h).