3. Empirical relations between SSTs and monsoon rainfall

The probable importance of the Gulf of California as the low-level moisture source for monsoon rainfall suggests that changes in the SSTs of the gulf waters may be an important factor to consider in predicting the interannual variability of the NA monsoon. To determine whether or not the SSTs may be important, a five year empirical study was conducted to explore the relationship between the values of SST in the gulf region and the amounts of rainfall observed over the adjacent land regions.

Since gulf SSTs generally peak in August, the period of greatest interest here is from the first onset of monsoon rainfall to just after the highest SSTs are reached, referred to herein as the warming phase. Data from six years, 1993-1997, and 1999, were examined to determine if there was any relationship between the values of SST and monsoon rainfall amounts. The data consisted of satellite multichannel SST (MCSST) data at 18 km spatial and weekly mean temporal resolution, along with satellite SSM/I five day cumulative (pentad) precipitation data having a spatial resolution of 0.25 x 0.25 degrees. The 1999 analysis represents a special focus on northern GOC SSTs and their relation to Arizona/New Mexico rainfall, as gulf regions further south were often obscurred by clouds. Daily resolution SST data was used, allowing us to test findings from the 1993-1997 analysis, and demonstrating the utility of these findings in forecasting flood conditions.

a. Satellite data

Fig. 3 Comparison between GOES-10 and mean weekly multichannel SSTs (horizontal bars) for part of the 1999 monsoon season, northern Gulf of California. The GOES SSTs are given every 3 hours when not obstructed by clouds, showing a strong diurnal cycle. Blank regions are due to cloud coverage.

To gain confidence in the use of the weekly mean MCSST data, we compared it with daily SST data from the GOES-10 imager and Pathfinder SSTs (also from AVHRR) provided by PO.DAAC. The GOES imager has channels at 0.52-0.72 µm, 3.78-4.03 µm, 10.2-11.2 µm, and 11.5-12.5 µm. For a description of the GOES SST algorithm and capabilities, see Wu et al. (1999). While weekly and daily Pathfinder SSTs are from NOAA polar orbiting satellites, making one ascending (daytime) and one descending (nighttime) measurement per day, the geostationary GOES satellites take images every 30 min., with a spatial resolution of 4 km (compared to 1.1 km from polar orbiting satellites). This allows coverage of the SST diurnal cycle, which can be up to 3°K over calmer seas (Wu et al. 1999). Figure 3 shows a comparison between GOES-10 SSTs observed every 3 hours, and weekly mean MCSSTs (horizontal bars), for the northern GOC. Blank periods were obscurred by clouds. N. gulf images containing less than 40 pixels were not used. Note that diurnal variations can reach up to 4°C. The higher MCSSTs were about 2°C higher than mean GOES values, and a -2 °C offset has been applied to the MCSSTs in Fig. 3. This problem has recently been acknowledged at JPL, and may be due to thermal contamination from land masses (Jorge Valdez, private communication). Over the SST range experienced in this study (24-32°C), a -2°C offset appears adequate for correcting the MCSSTs. This is seen more clearly in Fig. 4, where GOES SSTs have been averaged over a day to give mean daily values. Along with the weekly MCSSTs are plotted daily Pathfinder SSTs (dashed histograms). The limitation of SSTs from polar orbiting satellites now becomes apparent, as there were 10 days in the 59 day Pathfinder record where SSTs could not be retrieved, but could be retrieved by GOES-10. Moreover, Pathfinder SSTs were generally cooler, especially at lower temperatures, than GOES and adjusted MCSSTs. While difficult at this time to say which data source is most accurate, we used GOES SSTs and adjusted weekly MCSSTs in this study. The reduced cloud obstruction makes GOES SSTs attractive for use as a practical standard. Since GOES SSTs have only been archived since 1998, we used adjusted MCSSTs for the period 1993- 1997.

Fig. 4. Same as fig. 3, except GOES SSTs are averaged over each day, eliminating the diurnal cycle. Also shown are daily Pathfinder SSTs (dashed histograms).

Due to the low spatial resolution and questionable reliability of station precipitation data in Mexico, satellite SSM/I data were used to qualitatively assess the spatial distribution of rainfall over the monsoon region. Given the localized nature of convective precipitation, satellite measurements appeared most appropriate. There were generally three Defense Meteorological Satellite Program (DMSP) satellites operational during this period, making 2 to 6 overpasses per day regarding the SSM/I data (sun synchronous orbits), which should capture the diurnal cycle of convective activity. The approximate timing for the three ascending overpasses ranged between 17:35 and 21:06 LST (i.e. MST), spanning a period during which monsoon convection is known to be active (Gourley et al. 1998; Wes Berg, private communication), with at least one ascending pass per day over the monsoon region (100W-120W, 15N-38N). The SSM/I swath width is 1400 km, and the swath path is roughly parallel to the gulf axis. These rainfall estimates were only used on a relative basis.

b. Temporal and Spatial Evolution of SSTs and Rainfall

The results for each year are given in Fig. 6-10. Weekly SST variations are shown for each region, which roughly correspond to land regions to the N.E. or west (likely to be effected by southerly or onshore flow). Rainfall amounts per pentad (in cm) are shown for these regions during the SST warming phase. Warming phase here refers to the 1st rainfall jump above "background" ( 1.0 cm) to the time about 10 days after SSTs level off.

Results indicate that there is no evidence of a relationship between SST increases and rainfall amounts for SSTs < 26°C, so 26°C is viewed as a threshold value above which SST increases may lead to convection and rainfall. While this result is based solely on the analysis of this particular five year data set, the same SST-convection threshold of 26°C was reported by Zhang (1993) and Chaboureau et al. (1998) for tropical convective activity. Moreover, an analytical modeling study (McBride and Fraedrich 1995) has related Conditional Instability of the Second Kind (CISK) theory to underlying SSTs, and demonstrated how convective instability may manifest through two growth modes: a slow and a fast mode. The transition from slow to fast convective growth occurs at an SST threshold of about 25.5°C for the parameters chosen in their study. In view of this observational and supporting theoretical work, the lack of any convective activity associated with SSTs < 26°C within the gulf region is not surprising.

To aid data interpretation, this threshold value is shown by the dashed line in the SST plots in Fig. 6-10. SST increases are labeled chronologically as 1, 2, 3, etc., followed by A, B, C or D, corresponding to the pre-, S., C., or N. gulf regions, respectively. Only SST jumps > 0.4°C were considered to be important. For the 1993-1995 seasons, any rainfall increase occurring within 5 to 17 days after such an SST increase was attributed to that SST increase, and was labeled accordingly. The lag period for the 1996-1997 seasons was 1 to 15 days, based on histogram midpoints. These lag periods likely depend on wind and other conditions, and may be a function of the moisture surge events known as Gulf Surges (e.g. Hales 1972; Stensrud et al. 1997) or other phenomena which can transport boundary layer moisture poleward. Given prevailing wind directions, rainfall increases were never attributed to an SST increase north of the rainfall region.

Except for the 1996 season, no tropical depressions were evident north of about 20 degrees latitude (based on SSM/I and GOES infrared satellite images) during the warming phase, and hence were not responsible for rainfall during those periods. Three tropical depressions were identified after the warming phase, and are labeled "TD" in Fig. 7, 8 and 9. In 1996, about 10 days after the SST increase labeled 4A, 7B, 5C and 6D, a tropical depression appeared on the IR satellite images, and traveled up the axis of the gulf, becoming more organized and compact. It appeared to entrain surrounding moisture, but was confined mostly to the gulf in its later stages, with cyclonic winds moving moisture away from the Sierra Madres (especially in the N. Gulf). This may explain the diminished or lack of rainfall from this SST increase, especially in the N. Gulf and AZNM regions.

Possible examples of northward propagating rainfall events are shown by peak "1A" in Fig. 6, peak 3A/3B in Fig. 8, the TD peak in Fig. 8, three peaks associated with 3B, 4B, 5B/6B in Fig. 9, and three peaks associated with 1A, 6B and 5A/7B in Fig. 10. The data is consistent with other observations that indicate convection often originates in the southern or pre-gulf regions (Stensrud et al. 1997). Particularly interesting is the rainfall period associated with 1A in Fig. 10. Although significant monsoon rainfall in any of the 4 regions of Fig. 5 does not normally start until June or July, such rains began around May 7th in all 4 regions in 1997. This coincides with the timing of pre-gulf SSTs exceeding 26°C, exhibiting an increase of 2°C. There was no rainfall indicated for these regions during the previous month. Historical GOES satellite imagery shows strong convection in these 4 regions with upper-level winds apparently from the southwest or south, and indicated this rainy period, lasting at least 13 days, was not due to any organized weather system. Another example of early rainfall occurred in 1994 in association with SST increase 1A, beginning around May 22nd. Inspection of historical GOES satellite images reveals that a cut-off low, with little associated cloud cover, was drawing moisture off the S. gulf and possibly the pre-gulf regions, circulating it into AZNM, where it then organized into convective complexes. Some of these northward propagating convective complexes may be due to Gulf Surge events, which appear to be triggered by the passage of easterly waves (Stensrud et al. 1997), and transport moisture pulses up the gulf into Arizona. However, while a Gulf Surge may last up to 3 days, the above rainy period beginning about 6 May 1997 lasted 13 days or more. Gulf Surge events, and possibly other processes, may work in conjunction with SST increases in the southern and pre-gulf regions to free up boundary layer moisture for convection over land. The periodic nature of Gulf Surges, typically 9 day intervals but variable, may at least partially account for the lag periods apparent in the data here.

It is noteworthy that the heaviest periods of rainfall in AZNM occur after SSTs in the N. gulf attain about 29°C or higher. This is observed for all 5 seasons, and will be discussed more in subsection d.

c. SST-rainfall correlations in Mexico

Psst = (SST2 - SST1) (SST2 - 26.0) ,                 (1)

where SST2 is the highest SST during an SST increase, and SST1 is the value immediately preceding the increase. The physical rationale for this parameter is that both the magnitude of the increase (which may have a destabilizing effect on the atmosphere) and the temperature amount above the threshold SST of 26°C (which affects relative humidity) help to determine the rainfall amount.

Since SST fields and perhaps low-level prevailing wind directions vary from year-to-year, with SST-rainfall correlations between regions being seasonally dependent, each season was evaluated separately using its own lag correlation criteria during the warming phase, as well as the regions considered for calculating PSST and rainfall amounts. These criteria were chosen to yield the best correlation. For example, for 1994, SST jumps in both the pre- and S. gulf regions appeared to be most related to rainfall in the C. gulf region. Thus, SST jumps in the pre- and S. gulf regions were averaged and related to C. gulf rainfall amounts (cm) for pentad midpoints occurring 4 to 13 days after the SST histogram midpoint. If more than one region was used, the corresponding PSST or rainfall amounts in these regions were averaged. The results of this analysis for the five seasons are shown in Table 1.

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TABLE 1.  Conditions for deriving SST parameters and rainfall amounts.

         Regions used for    Regions used for rainfall     Lag period
Season   SST parameter        amount during lag period      (days)

1993     pre-gulf               S. gulf                       6-14

1994     pre- and S. gulf       C. gulf                       4-13

1995     pre- and S. gulf       C. gulf                       8-14

1996     S. gulf                C. gulf                       1-13

1997     pre-, S. & C. gulf     S. and C. gulf                0-15

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The results of this 5 season analysis are shown in Fig. 11, where there is a clear suggestion that rainfall amounts increase as PSST increases, yielding a correlation coefficient of 0.75. While an understanding of the causes of this relationship is needed, one possible explanation is that the variations in SST within the Gulf of California are playing a key role in the timing and amount of monsoon rainfall in northwestern Mexico. One could also argue that this relation is due to a cyclical change in cloudiness, unrelated to SSTs. For instance, during clear days the SSTs might increase, followed by a cloudy period when they didn't change, accompanied by rainfall over the Sierra Madres. However, while this explanation might explain the existence of a lag period between SST jumps and rainfall, it does not explain why a positive slope should exist between PSST and rainfall. Moreover, this explanation does not explain why significant rainfall commences only after SSTs exceed    26°C (note PSST 0 in Fig. 11).

Fig. 11 Rainfall amounts during lag periods related to corresponding SST jumps via the SST parameter, for the regions and lag periods described in Table 1.

d. Arizona-New Mexico rainfall dependence on northern gulf SSTs

It may be the sensitivity of convection to relatively high moisture levels that best explain Fig. 12 and other results in this paper. This is illustrated in Fig. 13, which describes results from an idealized situation. We assumed an SST jump of 1°C took place under a boundary layer 300 m deep. The relative humidity (RH) of the boundary layer air was assumed to be 80% relative to the saturation vapor density at equilibrium with the SST. Using the Clausius-Clapeyron equation, the increase in precipitable water (deltaPW) in the boundary layer for a 1°C SST jump was calculated over a range of initial SST values, ranging from 21 to 31°C. The SSTs in Fig. 13 are the initial SSTs prior to a 1°C increase. The PW increases (deltaPW) are given by the long-dashed curve. The total boundary layer PW (based on initial SSTs) is described by the short-dashed curve. The boundary layer air is assumed to arrive at cloud base undiluted. By equating the latent heat released via the SST induced vapor density change with the sensible heat increase of the air, the change in temperature near cloud base due to latent heat release can be estimated:

deltaT = RH ( Ro_vs2 - Ro_vs1 ) Lv / ( Ro_a cp_a ) ,                      (2)

where Ro_vs = water saturation vapor density, 2 and 1 denote after and prior to SST jump, Lv = latent heat of vaporization, Ro_a = air density at cloud base (assumed 700 mb pressure; 10°C), and cp_a = specific heat of dry air at constant pressure. deltaT is shown by the solid curve in Fig. 13. Note that deltaT results only from deltaPW (i.e. a given SST jump), and not the cumulative increase in total PW. Hence, the fractional increase of deltaPW and deltaT with increasing SST are identical.

Fig. 12 Arizona/New Mexico region cumulative normalized rainfall for periods having N. gulf SSTs < indicated SST. Time is implicit with increasing SSTs.

Fig. 12 suggests that convective activity over AZNM increases markedly after N. gulf SSTs exceed 27.5°C.

Fig. 13. Increase in precipitable water (delta PW, long-dashed curve) and cloud temperature (deltaT, solid curve) due to SST jumps of 1°C, where deltaT is due to latent heating only. A 300 m deep boundary layer was assumed with RH=80%. The total PW in the boundary layer is also shown (short-dashed curve).

Fig. 13 suggests that the latent heat released due to a 1°C SST jump is significant to convection by raising cloud temperature. It is possible that a delicate balance exists in regards to factors determining convection, such that a modest change in deltaT could produce conditions much more favorable for convection. Such reasoning appears consistent with the concept of a critical SST for rapid convection growth, as found from observations (Zhang 1993; Chaboureau et al. 1998) and theory (McBride and Fraedrich 1995; see Sec. 3b). The deltaT values in Fig. 13 are only rough estimates, with entrainment and smaller SST jumps producing lower estimates. A more realistic and comprehensive treatment of this issue is desirable but is beyond the scope of this study.