4.1. PWV and Precipitation Diurnal Cycles
In general, the WRF-GFS overestimates PWV
diurnal cycle, no matter whether the event is classified as a weakly or strongly forced day (Figure 3
a–c). However, at the last four hours of the forecast period, WRF-GFS PWV
values are drier than the GPS-derived PWV
values. Both for the combined and weak cases, the WRF-GFS PWV
values are around 0.6 mm less than the GPS-derived PWV
values. Even though the difference between the model and the observations is obvious, most of the time the WRF-GFS PWV
is within the standard error of the GPS-derived PWV
measurement, as shown by the shaded areas, except in the period of 0100 to 0400 UTC (1800–2100 LT). This is the time when diurnal precipitation is at its peak, as shown in Figure 3
The two maxima in the PWV
diurnal cycle correspond to the two peaks of precipitation. When precipitation occurs, the atmosphere is saturated with moisture from rainwater droplets and cloud droplets. The two maxima occur because of the timing difference in precipitation peak at some sites. The first PWV
maximum is associated with the first peak of precipitation, occurring around 2000 to 2200 UTC (1300–1500 LT) at MGDA and SA80 (Figures S1 and S2
). The second PWV
maximum, which occurs between 0000 to 0400 UTC (1700 to 2100 LT), is associated with the second peak of precipitation, similar to the finding by Nesbitt et al. [10
], which shows that a precipitation peak occurs between 1800 to 2000 LT.
There is a timing issue in the WRF-GFS simulations. We note in Figure 3
a that the WRF-GFS PWV
values decrease to the minimum, from 40.99 mm to 40.66 mm, within four hours of 1900 UTC (1200 LT) to 2300 UTC (1600 LT), while the GPS-derived PWV
values decrease from 40.53 mm to its minimum, 40.09 mm, in five hours from 1900 UTC (1200 LT) to 0000 UTC (1700 LT). As a result, the WRF-GFS simulations reach the PWV
minimum an hour earlier than the GPS-derived PWV
does, creating an hour lag between the WRF-GFS PWV
diurnal cycle and the GPS-derived PWV
diurnal cycle. This holds true for weakly forced days (Figure 3
b) and strongly forced days (Figure 3
In Figure 3
a, the WRF-GFS simulations rapidly increase the PWV
values from 40.66 mm at 2300 UTC (1600 LT) to maximum 41.60 mm at 0300 UTC (2000 LT) while the observations exhibit a slower increase over a longer time period, from 40.09 mm at 0000 UTC (1700 LT) to maximum 40.92 mm at 0900 UTC (0200 LT). As a result, the WRF-GFS PWV
diurnal cycle reaches the second maximum around six hours earlier than the GPS-derived PWV
. Thus, the WRF-GFS PWV
becomes more out of phase, compared with the GPS-derived PWV
diurnal cycle, during the late afternoon to evening hours. At this time, WRF-GFS PWV
values go beyond the range of the GPS-derived PWV
standard error. Similar time lags and overestimation are also observed both in the weakly forced days (Figure 3
b) and the strongly forced days (Figure 3
The only noticeable difference between the weakly and strongly forced days is the amount of hourly WRF-GFS PWV
in the last six hours of the forecast. The weakly forced days (Figure 3
b) exhibit a rapid decrease, from 41.40 mm to 39.60 mm, in the last six hours of forecast. The final WRF-GFS PWV
value is almost out of the range of standard error. The strongly forced days (Figure 3
c), on the other hand, show a slow decrease from 43.50 mm to 41.75 mm, within the same period. The final WRF-GFS PWV
value is within the range of standard error and close to the final GPS-derived PWV
value. The difference is greater on the weakly forced days than on strongly forced days.
The rapid decrease in WRF-GFS PWV
corresponds to the early termination of convective precipitation (Figure 3
d–f). The WRF-GFS precipitation for all cases is within the standard error of the rain gauge measurement, from about 2200 to 0200 UTC (1500 to 1900 LT). The modeled values are closer to the rain gauge than to the GPM Final product, whose values fall outside the range of standard error of the rain gauges. After 0200 UTC (1900 LT), the amount of precipitation decreases rapidly, from 0.65 mm at 0200 UTC (1900 LT) to less than 0.1 mm at 0600 UTC (2300 LT), and exceeds the standard error, just as the WRF-GFS PWV
decreases rapidly (Figure 3
a). This behavior is basically the same for the weakly and strongly forced days. While the rain gauge and the GPM Final still indicate ongoing precipitation after 0500 UTC (2200 LT), the amount of WRF-GFS precipitation is close to zero. This low value marks the end of the convective precipitation in the simulations. This early termination issue in the WRF-GFS precipitation is consistent with Moker et al. [8
Unlike in the WRF-GFS simulations, the WRF-NAM simulations overestimate the PWV
diurnal cycle throughout the forecast period, so that their values exceed the standard error (Figure 4
a–c). This high bias holds true for the weakly and strongly forced days. At the initial forecast hour, the mean difference is more than 3.00 mm for weakly forced days, strongly forced days, and the combination of both. At the end of the forecast hour, the difference is around 1.00 mm for all cases. The WRF-NAM PWV
diurnal cycle contains only one minimum and one maximum. The maximum in the first 12 h of forecast is not well defined.
Similar to the WRF-GFS, the minimum and the maximum of the PWV
diurnal cycle in the WRF-NAM are out of phase compared with those of the GPS-derived PWV
diurnal cycle, due to rapid decrease and rapid increase within 12 h of forecast. The WRF-NAM PWV
in Figure 4
a reaches the minimum of 41.72 mm at 2100 UTC (1400 LT), compared with the GPS-derived PWV
minimum at 0000 UTC (1700 LT), as shown earlier. Thus, it creates a three-hour lag within the 12-h forecast. The strongly forced days (Figure 4
c) also exhibit higher PWV
values throughout the diurnal cycle than the weakly forced days or the combination of both. The difference between the initial WRF-NAM PWV
value and the GPS-derived PWV
value almost reaches 4.00 mm. However, the strongly forced days do not exhibit any time lags, since the minimum of WRF-NAM PWV
and GPS derived PWV
diurnal cycle occurs at 2300 UTC (1600 LT).
The high bias of WRF-NAM PWV
generates precipitation as early as the first forecast hour at 1300 UTC (0600 LT), as shown in Figure 4
d–f. This model precipitation exceeds the standard error of the rain gauge measurements. The WRF-NAM precipitation values come to the standard error range at 2100 to 0100 UTC (1400 to 1800 LT), even though overestimation occurs within the period. Similar to the WRF-GFS simulations, this model, in all cases, also exhibits rapid decrease in precipitation after 0200 UTC (1900 LT), marking early termination of convective precipitation.
In summary, both the WRF-GFS and WRF-NAM simulations generate higher values in the PWV
diurnal cycle at the initial forecast hour than the GPS-derived PWV
. This result agrees with that of Moker et al. [8
], where wet bias was present in Transect 2013. While the WRF-GFS PWV
is generally within the range of the standard error of observations, WRF-NAM PWV
is out of range of the standard error. The time lags and the rapid decrease of WRF-GFS PWV
result in early termination of the WRF-GFS precipitation. It is also notable that WRF-GFS precipitation is closer to rain gauge measurements than to satellite precipitation products. The overestimation of WRF-NAM PWV
generates an early initiation and termination of modeled precipitation, with high positive bias.
4.2. Precipitation Diurnal Cycle in the Domain
While Figure 3
d–f and Figure 4
d–f show the mean diurnal cycles of precipitation across 14 observation sites, Figure 5
and Figure 6
exhibit the mean diurnal cycle of precipitation rate across the region (first row) and its bias (third row), with respect to the GPM Final precipitation products (second row). The display of these figures and the bias calculation are similar to those in Moker et al. [8
]. The difference is that the study by Moker et al. [8
] finds no statistically significant bias between the strongly and weakly forced days in Transect 2013. In our study, the bias at 0900–1200 UTC between the strongly and weakly forced days is statistically significant in the WRF-GFS simulations. For simplicity, we present the combined set of days for both the WRF-GFS and WRF-NAM simulations.
The WRF-GFS simulation (Figure 5
) shows dry bias (−0.05 mm h−1
) in the initial period (1200–1500 UTC). This negative bias remains for the next two periods (1500–1800 UTC and 1800–2100 UTC), with mean bias values of −0.02 mm h−1
. The precipitation in the WRF-GFS simulation begins in the 1800–2100 UTC period in the eastern slopes and high terrain of SMO. The timing of the precipitation onset more or less matches the GPM Final precipitation estimate, as seen on the second row. However, Figure 3
shows that the model initiates precipitation about an hour late with respect to the rain gauge observations.
Starting in the 2100–0000 UTC period, the mean bias becomes more negative, especially around the mouth of GoC and the slopes of SMO to the east of TNTB. The convective systems that propagate toward the gulf and affect the coastal area (e.g., KINO and TNTB) and the western slopes of SMO are not resolved by the WRF-GFS simulation, as seen in the 0000–0300 UTC period. Instead of developing and propagating westward, the model reduces the intensity of the precipitation, as marked by a large area of negative bias occurring along the coast of the GoC, expanding from ITS1 to the south of TNTB and along the western slopes of SMO. After this period, the WRF-GFS model generates a precipitation rate less than 1 mm h-1, as seen in 0300–0600 UTC panel. This reflects a relative lack of westward propagation of the convection. In the 0600–0900 UTC period, the WRF-GFS simulations completely terminates the precipitation in the western slopes of SMO, while the GPM Final precipitation rate estimate still shows the ongoing convective systems moving across GoC toward Baja California.
The WRF-NAM simulations (Figure 6
) have high positive biases in the area around TNHM, MZTN, USMX, RAYN, and OPDE at the initial hour, which corresponds to the high WRF-NAM PWV
, and precipitation values relative to the GPS-derived PWV
and rain gauge measurement mentioned in the previous section. The overall mean bias across the grids in the WRF-NAM simulations is 0.11 mm hr−1
in this early period of 1500–1800 UTC, which is much higher than that of the WRF-GFS in the same period.
When compared with the GPM Final precipitation rate estimate, the peak of the mean precipitation rate in the WRF-NAM occurs in the 2100–0000 UTC period, 3 h earlier than the GPM Final precipitation estimate. In the 0000–0300 UTC period, the WRF-NAM simulation also does not resolve convective organization and propagation westward. Instead, it reduces the precipitation rate, resulting in a dry bias, especially in the western slopes of SMO (e.g., YESX). The mean dry bias continues to increase by 4 mm h−1 in the 0300–0600 UTC period along the eastern seaboard of GoC and the western slopes of SMO. The model does not resolve the remnant convective systems that propagate toward the GoC in the late evening to early morning hours, as captured by GPM Final precipitation estimate in the 0600–0900 UTC period.
The GPM Final precipitation estimate contains bias with respect to the rain gauge measurements, as shown in Section 2
and in sub Section 3.1
. Thus, the bias calculation of the model precipitation rate, with respect to the GPM Final precipitation rate estimate, contains substantial uncertainty. We found that the WRF-GFS simulations initiate convective precipitation about an hour late with respect to rain gauge observation, but in the same hour with respect to the GPM Final precipitation estimate. Contrastingly, the WRF-NAM simulations initiate convective precipitation much earlier than rain gauge and GPM Final observations. Both WRF-GFS and WRF-NAM terminate the convective rain over the slopes of SMO too early when compared with the rain gauge and GPM Final observations. This early initiation and termination of the diurnal precipitation cycle in WRF has been found in a number of studies, such as Vincent and Lane [65
] who show that the diurnal cycle of precipitation over the Maritime Continent during the Madden–Julian Oscillation passage occurs 4 to 5 h earlier than the observed precipitation cycle. The models also underestimate the westward propagation of the convective system, irrespective of the lateral boundary forcing, as also found by Moker et al. [8
]. They also become drier in the period of peak precipitation (0000–0300 UTC), and at the end of the forecast hours, than the GPM Final and rain gauge measurements. A similar propagation issue has also been found by Hassim et al. [66
], over New Guinea. The study shows a possible link between the propagation of the convective system and the early initiation of precipitation due to atmospheric conditions such as gravity waves, mid-level tropospheric moisture, and low-level moisture convergence.
4.3. Model Precipitation Skill Analysis
In Figure 7
and Figure 8
, the CSI, POD, and FAR metric differences of the WRF-GFS and the WRF-NAM models, respectively, are displayed. Each shows the precipitation forecast skills of the WRF models. Blue (red) indicates the increased forecast skills for strongly (weakly) forced days. Field significance is displayed on the bottom left and the pattern correlation between the 6-hourly and the daily forecast metrics is on the bottom right of each panel.
Both models generally have similar patterns in each time period, but there are different details in each. In the 24-h period, the models exhibit increased forecast skill in strongly forced days in the western slopes and high terrain of SMO. However, the CSI
differences in the WRF-GFS appear to be lesser than those in the WRF-NAM simulation, as seen in Figure 7
j,k, and Figure 8
j,k. The FAR
difference between the two models is similar. This implies that the forecast skill along the western slopes of SMO during strongly forced days is better than during weakly forced days. Both models do not perform well in forecasting precipitation during weakly forced days over the western slopes of SMO and the coastal areas.
In the 1800–0000 UTC period, the CSI
differences in both models are statistically significant, but not the FAR,
difference. The correlations in the CSI
differences between this period and the daily period are also higher than that of the FAR
. As displayed in the CSI
, and FAR differences (Figure 7
a–c, Figure 8
a–c), the forecast skill of the WRF-GFS and WRF-NAM during strongly forced days is better than weakly forced days, particularly in the western slopes of SMO (e.g., MZTN, YESX, ITS1).
In the 0000–0600 UTC, the CSI
differences of the WRF-GFS (Figure 7
d,f) are not field statistically significant, while the CSI
, and FAR
differences in the WRF-NAM (Figure 8
d–f) are field statistically significant. The correlation values for all the differences are greater than +0.2. In general, both models exhibit better forecast skill during strongly forced days over the western slopes of SMO, and some parts of the coastal area. The FAR
difference shows similarity for both simulations, but the WRF-NAM has higher correlation with the daily pattern.
In the 0600–1200 UTC period, the POD
metric difference in the WRF-GFS is field statistically significant (> 90%). The other metric difference is between 80% and 90%, except the FAR
difference in the WRF-NAM (Figure 8
i). The differences of the metrics between the strongly and weakly forced days are near zero for both model simulations. High forecast skills during strongly forced days are shown in the WRF-GFS and WRF-NAM simulations over the SMO eastern slopes and its high terrain.
In summary, the WRF-GFS model exhibits higher forecast skills over the western slopes of SMO and the coastal area during strongly forced days in which the IV is present near or within the monsoon core region. The WRF-NAM model has high forecast skills over both the high terrain of SMO and the coastal areas during strongly forced days. Yet, in general, both models are more challenged to forecast and propagate MCS development during weakly forced days. This finding confirms the results of Transect 2013 in Moker et al. [8
4.4. Sensitivity Analysis
Finally, we compare the mean sensitivity of the WRF-GFS PWV, precipitation, and QCONV across the domain, relative to the GPS-equivalent WRF-GFS PWV at the initial condition on the weakly forced day of 9 August, with those on the strongly forced day of 27 July. These two cases are taken for this analysis because both represent the characteristics of heavy monsoon precipitation based on the rain-gauge measurement in several sites, the extent of the convective clouds, and the dynamic pattern of the winds.
On the strongly forced day (27 July), the winds in the 2-PVU layer (dynamic tropopause) turn counterclockwise inside the monsoon core region at 1200 UTC. It is a clear indication of the IV presence. This cyclonic turning generates a PV anomaly, indicated by 2-PVU layer lowered to around 260 hPa over the northern and eastern SMO (Figure 9
c). As a result, the static stability decreases due to the upward tilting of the isentropes, thus, the environment is favorable for rising motion. Mature mesoscale convective system is developed to the northeast of the IV location at 0300 UTC on 28 July, as captured by GOES 15 WV (Figure 9
a). The rain gauges in TNHM and MZTN measure 21.73 mm and 10.85 mm, respectively, at 0300 UTC, and in SA80 measures 32.26 mm at 0400 UTC.
On the weakly forced day (9 August), the 300-hPa layer does not contain cyclonic wind and the 2-PVU layer does not indicate any PV anomaly at 1200 UTC (Figure 9
d). There is no IV presence. The pressure on the dynamic tropopause within the monsoon core region is almost uniform, ranging from 100 to 160 hPa. In the presence of daily surface heating and water vapor content in the atmosphere, a convective system starts to organize at 2100 UTC over the western slopes of SMO. The convective system reaches a mature stage at 0300 UTC on 10 August, with less than 190-K cloud-top temperature, indicating strong updraft occurring in the system (Figure 9
b). The rain gauges at MZTN and TNHM measure 44.41 mm and 32.41 mm, respectively, from 0300 UTC to 0600 UTC. Even though the synoptic forcing is clearly different between these two days, both have clear MCSs that are of nearly identical size and occur in basically same location over Sonora.
We compute the mean sensitivity based on the topographical classification, i.e., mountainous sites and coastal sites, as shown in Figure 1
and explained in Section 3.3
. The results show that the PWV
in the domain is more sensitive to the change in initial PWV
across the coastal sites than across the mountainous sites, both during the weakly forced day and strongly forced day, as shown in Figure 10
On the weakly forced day, the PWV
is most sensitive over the northern part of SMO (Figure 10
c). A hundred mm change of initial PWV
in the coastal sites produces a 5 mm or more increase of PWV
in the area at those hours. A highly negative sensitivity occurs at 0000 UTC in the eastern slopes of SMO. This means that a 100 mm change in initial PWV
in the coastal sites generates around a 5 mm or more decrease of PWV
in the area at that hour. On the strongly forced day, the PWV
is negatively sensitive across the northern part of SMO. This means that a 100 mm change of initial PWV
in the coastal sites reduces the PWV
in the region by around 5 mm (Figure 10
The statistically significant dominant mode, generated by the covariance-based EOF analysis (Figure 10
a,d) at 0000 UTC, agrees with the mean sensitivity of PWV
for both weakly and strongly forced days, in Figure 10
c,f, respectively. The pattern in Figure 10
a resembles the pattern in Figure 10
c, with a correlation value of 0.25. The area of positive percentage is situated across the northern SMO, stretching to east-northeast with area of negative percentage just to the south. The covariance-based EOF analysis confirms that the WRF-GFS-equivalent initial PWV
in the coastal sites influences the PWV
across the domain in the later forecast hours more than the initial PWV
in the mountainous sites.
For the strongly forced day, the pattern in Figure 10
d resembles the pattern in Figure 10
f, with a pattern correlation value of 0.77. The area with negative percentage is spreading west to east over the northern SMO, with positive percentage area to the north and the south. Similar to the weakly forced day, the covariance-based EOF analysis for the 27 July case shows that the WRF-GFS-equivalent initial PWV
in the coastal sites affects the PWV
in the domain in the later forecast hours more than the initial PWV
in the mountainous sites. Therefore, the dominant mode of sensitivity separates the mean sensitivity of the mountainous sites from the coastal sites.
The sensitivity analyses for the precipitation produces contrary results when compared to the PWV
. The change of precipitation across the domain in the later forecast hours during the weakly forced day is more sensitive to the change of the initial PWV
in the mountainous sites than that in the coastal sites, for both strongly and weakly forced days (Figure 11
The impact of the initial PWV
change in the mountainous sites versus the coastal sites to the precipitation across the domain during the weakly forced day is shown around the peak of precipitation, at 0000 UTC and 0300 UTC (Figure 11
a,b,e,f). Over the western slopes of SMO, a millimeter change of initial PWV
in the mountainous sites generates a 0.1 mm or more increase of precipitation around USMX, MZTN, ITS1, YESX, TNCU, and over SMO in general (Figure 11
e,f). The change in initial PWV
in the coastal sites (Figure 11
a,b), on the other hand, does not generate as great an increase as the mountainous sites. Similarly, on the strongly forced day, the change in precipitation across the domain is more sensitive to the change in initial PWV
in the mountainous sites (Figure 11
g,h) than in the coastal sites (Figure 11
c,d). The sensitivity difference is clear over the northern slopes of SMO.
The mean of absolute values across the domain on each panel quantitatively indicates the distinct influence of the model-equivalent initial PWV of each class on the change of precipitation across the domain. The mean sensitivity for the mountainous sites is higher than that for the coastal sites. This is true for both weakly and strongly forced days. These quantitative values confirm that the WRF-GFS-equivalent initial PWV in the mountainous sites induces a greater influence on the change of precipitation across the domain in the later forecast hours than it does in the coastal sites. In a larger context, this fact also means that the convective organization and propagation across the domain is more sensitive to the initial PWV over the mountainous areas than the coastal areas.
The sensitivity analyses of QCONV (Figure 12
) are consistent with those of precipitation. The QCONV across the domain is sensitive to the change in initial PWV
in the mountainous sites more than in the coastal sites during the weakly and strongly forced days. The difference is particularly visible from 0000 UTC and 0300 UTC, where the increase of QCONV is situated around KINO, TNHM, MZTN, YESX, and ITS1, on the western slopes of SMO.
On the weakly forced day, a millimeter change of initial PWV
in the mountainous sites creates an increase of QCONV as much as 0.02 kg kg−1
e,f). In the mean QCONV sensitivity across the coastal sites (Figure 12
a,b), the increase signature of QCONV is hardly apparent. However, the mean of the absolute values across the domain reveals that the change of WRF-GFS-equivalent initial PWV
over the mountainous sites affects the change of QCONV across the domain more it does over the coastal sites. During the peak of the monsoon precipitation around 0000 UTC, the mean of absolute values of the QCONV sensitivity, relative to the WRF-GFS-equivalent initial PWV
over mountainous sites, is 9.2 × 10−4
, whereas the mean of absolute values of sensitivity relative to the WRF-GFS-equivalent initial PWV
over the coastal site is only 6.8 × 10−4
As seen from this pattern, there is minimal difference in QCONV sensitivity between the mountainous (Figure 12
g,h) and coastal sites (Figure 12
c,d) during the strongly forced day. The mean of absolute values across the domain at 0000 UTC, for example, is 1.5 × 10−3
for the sensitivity, relative to the change in WRF-GFS-equivalent initial PWV
in the mountainous sites, and 9.2 × 10−4
for the sensitivity relative to the change in WRF-GFS-equivalent initial PWV
in the coastal sites. Similar to the weakly forced day, the change in QCONV across the domain during the strongly forced day is more sensitive to the change in WRF-GFS-equivalent initial PWV
in the mountainous sites than in the coastal sites. Therefore, mountainous regions matter in terms of convective initiation and precipitation.
There are two questions to answer: (1) Why does changing initial PWV
in the coastal sites generate changes in PWV
across the domain more than changes in the mountainous sites? (2) Why does changing initial PWV
in the mountainous sites produce more changes in precipitation and QCONV across the domain than changes in the coastal sites? To answer the first question, we hypothesize that there is positive correlation between the initial PWV
in the coastal sites and PWV
across the domain, since the GoC is the moisture source of the domain. Therefore, the WRF-GFS model confirms what has been found by Adams and Comrie [4
] that the moisture during NAMS partly comes from the GoC, and, thus, an increase in PWV
in the coastal site will result in an increase of PWV
across the domain in the later forecast hours.
For the second question, the answer is that mountainous topography naturally induces convective initiation. Daily solar heating on its surface develops thermal differences between the mountain and the surrounding atmosphere, and upslope winds during daytime help water vapor to rise and condense. Both mechanisms create instability and assist convective initiation over mountainous regions. Thus, an increase in PWV
in the mountainous sites does increase the precipitation and QCONV on the western slopes of SMO and the northern part of SMO, as shown in the Figure 11
and Figure 12
. Moreover, since the convective system propagates westward, the change in initial PWV
in the mountainous sites also affects the change in precipitation and QCONV in the coastal areas at the later forecast hours. Similar results appear in other modeling studies, showing that an increase in precipitation in mountainous regions, such as Kilimanjaro and the Andes mountain ranges in Chile, is closely related to a change in the ambient condition and variables such as the geometry of the location, with respect to wind flows, as well as an increase in water vapor and temperature [60