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The North American Monsoon is a sharp seasonal rainfall that occurs in northwestern Mexico and southwestern US in July through September. The low level thermal low and upper level ridge entrenches themselves in that region, adjusting atmospheric circulation to increase southerly flow that carries moisture into the region. Moisture flux convergence thus occurs, due to moisture advection and increased thermodynamic instability as well as orographical forcing of the mountainous terrain. Studies have been conducted to determine the moisture sources and understand the physical mechanisms of the North American Monsoon as well as the well known Indian Monsoon. Researchers have attempted to explain the variability of these monsoons in relation with the snow cover of the neighboring mountain ranges and the sea surface temperatures (SSTs) in the Pacific and Indian Oceans. In the case of the Indian monsoon, an abrupt reversal of winds occurs at the onset of the monsoon, and the onshore flow bringing heavy rainfall to the western Indian coast. Climatologists have used the Blanford Hypothesis to explain the phenomenon, saying that the neighboring snow cover from antecedent winters works to adjust the land-sea temperature gradient. According to this hypothesis, above normal snow cover would weaken the monsoon due to a reduced land-sea temperature gradient. However, in subsequent studies, questions surrounding the Blanford Hypothesis have been raised due to conflicting results. Some studies have attempted to link the Indian Monsoon to ENSO with questionable results. In this study, an attempt is made to explain any possible linkages between the North American Monsoon, snow mass of the US and Canadian Rockies for the land-sea temperature gradient, and the Pacific SSTs for moisture sources. The snow mass is the melted equivalent of the snow depth; this adjustment being known as the snow-water equivalent (SWE). In other words, the SWE is the equivalent of the depth of the melted snow. This distinction is used throughout this paper. The El-Nino & Southern Oscillation (ENSO) index of the Nino-3.4 region and the Pacific Decadal Oscillation (PDO) index are used in this investigation. Precipitation, ENSO-3.4, and the snow depth data is acquired from the North American Regional Reanalysis (NARR) observational dataset while the PDO data is acquired from the National Centers for Environmental Prediction of the National Oceanic & Atmospheric Administration (NOAA-NCEP). In an attempt to find the driver of the monsoon, statistical and lead-lag analysis is used to determine or infer the relationships between the three climatological phenomenon and their anomalies.

The southwestern United States, particularly New Mexico, Arizona, southeastern California, Utah, and Nevada, gets most of their yearly precipitation in their monsoon season, which lasts from late June to late September (Ropelewski et al, 2005). This monsoon is known as the North American monsoon, which is a seasonal shift of upper and low level pressure and wind patterns that brings moisture into this region. The North American Monsoon has the elements of the well-known Indian Monsoon on a smaller scale (Ropelewski et al, 2005). However, there are variations in this monsoon that may be associated with periodic droughts and flooding episodes in the southwestern US. Another widely-known phenomenon closely related to the North American Monsoon is the Indian Monsoon, which brings heavy rainfall and disastrous flooding into western India during the summer months. The winds associated with the monsoon flow from the warm waters of the Indian Ocean onto the hills of western India. Warm ocean waters are conducive to high evaporation rates, and atmospheric flow that carries the moist air over hilly and mountainous landmasses and/or converges with another moist air mass is known as moisture flux convergence. During the summer months, moist air flows from the Indian Ocean onto the hilly lands of western India. As a result, air rises via orographical forcing and/or low level convergence, inducing convection and heavy rains over India.

These physical mechanisms also apply to the North American Monsoon as the terrain in southwest US and northwestern Mexico is fairly mountainous, and the sea surface temperatures of the neighboring Pacific Ocean and Gulf of California waters upstream of atmospheric flow are warm as well. Both monsoons occur only in summer, when the wind direction and strength are favorable for monsoon formation. At other times of the year, the atmospheric flow is often reversed. This reversal is remarkable in the case of the Indian Monsoon. During winter, winds flow directly from the land to sea, until the onset of the monsoon when offshore winds abruptly reverse direction and begin to flow onto land from the ocean. Regions affected by monsoons often are prone to severe flooding and drought, which has implications on the water supply and resources for the regions’ inhabitants. Safety issues also arise, as flash flooding is hazardous and disruptive.

Both the Indian and North American Monsoons and their high-to-low frequency variability have been studied by several climatologists, and causes of the monsoon variability have been hypothesized. One notable hypothesis, the Blanford Hypothesis, put forth the theory that the snow cover of a neighboring region from the winter antecedent to the monsoon season has an influence on the monsoon onset and strength. Specifically, Blanford Hypothesis postulates that an inverse relationship exists between the winter-spring snow cover in the Himalayas mountain region and June-September Indian rainfall. The North American Monsoon has a distinct onset, which varies from late June to early August and thus has a tremendous effect on July rainfall anomalies, particularly for the Southwest US and is accompanied by significant changes in large-scale atmospheric circulation. Ropelewski has found that, to a first approximation, the reversals of low level temperature gradients are initiated by differential heating between a land mass and adjacent ocean associated with the changes in seasons. A surface low-pressure system also accompanies the development of an upper-level monsoon anticyclone. Important roles in providing moisture to the North American Monsoon are played by the Pacific Ocean, Gulf of Mexico, and the Gulf of California. However, the north-south configuration of the mountain ranges (around 2000 m in elevation) in the Southwest US and western Mexico adds to the complexity of the moisture source debate, which remains unresolved to date. Ropelewski explains the complexity of the issue of moisture transport: the western slopes of the Sierra Madre Occidental channel and confine low-level flow from the south-southeast up the Gulf of California into the Southwest US. The eastern slopes of the Sierra Madre Mountains provide a barrier to low-level flow and direct low-level moisture transport from the Gulf of Mexico into the monsoon region. The topography of Mexico also vertically transports moisture higher into the troposphere by triggering convection associated with orographically triggered thunderstorms (Ropelewski et al, 2005). The Sierra Madres complicates the low-level (below 700 hPa) circulation patterns over the NAM region, leading to some debate as to the source of moisture for the NAM rainfall.

Inspired by the Blanford Hypothesis, past research (Matsui et al, 2002; Hawkins et al, 2002) has shown possible connections between the North American monsoon and the winter- through spring-time snow-cover over the US Rockies. These studies involving the snow-cover extent hypothesized that an inverse relationship does exist between the snow-cover of the US Rockies from winter through early summer and the magnitude of the monsoonal precipitation in the southwestern US. Higgins and Shi (2000) also have cited several studies that found that excessive (deficient) snow in the west-central United States leads to deficient (abundant) summer rain in New Mexico. The reasoning behind the Blanford Hypothesis is that the radiative properties of excess snow cover preceding the onset of the monsoon reduces the land-sea temperature gradient, and thus reduces the atmospheric geopotential thickness gradient between the land and the sea. At latitudes far from the equator, a geopotential gradient is balanced by the Coriolis force, resulting in geostrophic flow. However, at latitudes near the equator, a thickness gradient would actually result in a wind that flows directly down the geopotential gradient. Since India is of marginal distance from the equator and the Indian Ocean SSTs are nearly constant throughout the changing seasons, the land-sea temperature gradient induces a mean flow that reverses direction with the drastic land temperature oscillations as the seasons change. However, the effect of the snow cover-induced land-sea temperature gradient on the monsoon is debatable. While it is not clear how much the snow cover contributes to the steepness of the land-sea temperature gradient especially at the onset of the monsoon season, it is understood that snow cover increases the albedo of the Earth’s surface, and excessive snow cover reduces the absorption of solar radiation by the land surface, delaying the increase of land surface temperature well into late summer.

Past studies have been somewhat contradictory in some of their results. Three possible problems arise. One possible problem is that past studies were unable to determine the moisture source of the North American Monsoon, or at least determine the actual contribution of moisture to the NAM by all possible upstream moisture sources, such as the Gulf of California, North Pacific, tropical or equatorial Pacific, and the Gulf of Mexico. Without knowing precisely which moisture sources are of importance and which contributes little to the NAM makes investigation of the rainfall anomalies associated with the variability of the monsoon difficult and inconclusive. A second problem is that the studies have left out a potentially important variable, snow depth, which may be one of the factors impacting the monsoonal precipitation or the onset of the monsoon season. Snow depth is not the same as snow cover, because snow cover in data form only tells how much of an area is covered with snow and gives no indication of the mass or depth of the snow overlying that land area. The mass of snow is measured in snow water equivalent (SWE) units. SWE is a measure of the water content of snow, when a column of snow was melted into liquid phase, which is then measured in the units of millimeters. Water has unusually high heat capacity for a fluid, so that after winters with positive snowfall anomalies, abnormally large amounts of solar and long-wave radiation are required to melt the snow before the surface could be heated directly. Snow depth anomalies may impact the surface energy budget in a way such that positive soil moisture anomalies tends to decrease the surface temperature, which is known as a soil moisture–surface temperature negative feedback. However, above normal soil moisture may also increase evaporation rates. Increased evaporation rates may then lead to increased moisture convergence which in turn leads to increased precipitation. This feedback loop is known as the soil moisture – rainfall positive feedback. Various studies in the past (including Hawkins and Matsui) have attempted to determine which of the competing feedback loops have a stronger effect on the North American monsoon, only with mixed results. Additional studies have also discussed the possible thermal effects on the atmospheric thickness via snow-albedo and/or radiative cooling feedbacks. A third problem arises when the effects of Pacific SSTs on snow accumulations in the west-central US and Canada are considered. Wet (dry) summer monsoons in the Southwest US tend to follow winters characterized by dry (wet) conditions in the Southwest US and wet (dry) conditions in the northwestern US. This association was attributed to the wintertime pattern of Pacific SST anomalies, which provide an ocean-based memory source of antecedent climate fluctuations that affect the amount of rainfall in the NAM system (Higgins & Shi, 2000).

Other research (Castro et al, 2001) investigated a possible linkage between Pacific Ocean sea surface temperature (SST) anomalies and the North American monsoon. The monsoon in the southwestern US, in near proximity to the Pacific Ocean, may be influenced via oceanic and atmospheric teleconnections such as the El-Nino & Southern Oscillation (ENSO) and the Pacific Decadal Oscillation (PDO). The ENSO is the variation of equatorial Pacific SSTs off the west coast of South America stretching into the West Equatorial Pacific. The ENSO is a widely known oceanic phenomenon that has perturbed the climate in many regions around the globe. The PDO is also an oceanic phenomenon with varying SSTs located in the North Pacific much further from the equator all the way northward to Alaska. During ENSO and PDO events, the anomalous SSTs vary on interannual to decadal time scales, respectively. These time scales may be fitting for the variations in the North American monsoon, because as Matsui (2002) found, there was a strong correlation between the monsoon and snow-cover only in the time period of 1961-1990, only to have this linkage break down outside of that aforementioned time period.

The relationship between the North American Monsoon and the spring snow-cover extent in the US Rockies will be investigated using the North American Regional Reanalysis (NARR) observational dataset at 1° x 1° grid resolution, within the spatial domain of latitudes 20°N – 60°N and longitudes of 140°W – 100°W, and a temporal domain of 1979-2002 on a monthly time scale. Another dataset, ECMWF ERA-40 Reanalysis, 2.5° x 2.5° grid resolution with the specified spatial and temporal domains, will also be used for comparison purposes. One snow-related variable will be of importance: snow depth, measured in millimeters (mm) SWE. This variable is not a measurement of snow depth in frozen form, but taken after melting a column of snow and measuring the depth of the water from melted snow. Snow-to-water ratios are usually 10 to 1, but may vary depending on how much moisture is present in the snow and what the temperature was when the snow had fallen. April is the selected month to represent the approximate snow depth that accumulated throughout the entire winter. Investigating the snow depth would not only reveal the snow-cover extent, but also the amounts of snow that covered the Rockies adjacent to the monsoon region. This may yield clues to how much radiative energy is used to melt the snow rather than directly heat the surface. Matsui and Hawkins has also suggested that positive snow depth anomalies may be linked to a delay in the onset of the monsoon season caused by a delay in surface heating and moisture convergence. Another variable of importance includes convective precipitation, measured in millimeters per day (mm/day), also available in the NARR dataset. Convective precipitation in the North American Monsoon occurs from July to September, so the months July, August, and September are selected for analysis on monsoonal precipitation.

Pacific SST data include the ENSO index that covers the 3.4 region that overlaps regions 3 and 4, and the Pacific Decadal Oscillation (PDO) index. The standardized PDO index is available via PDO text-formatted indices from the National Centers for Environmental Prediction of the National Oceanic & Atmospheric Administration (NOAA-NCEP). The ENSO-3.4 index is constructed using the NARR dataset, and then was annually averaged into yearly values from 1979 to 2002. Because the PDO index date much further back from 1979, monthly index data from April 1978 to April 2002 and all the months in between was spliced from the original index from NCEP. The spliced indices were recalibrated by computing the average value from April 1978 to April 2002 and then subtracting this average value from the actual values of the spliced indices. These annually averaged April ENSO and PDO indices will be used in conjunction with the April SWE index, while the annual averaging procedure would be repeated to construct annually averaged August ENSO and PDO indices to be used in conjunction with the monsoonal precipitation JAS indices. This procedure ensures proper lead-lag analysis on the order of four to six months prior to the monsoon. The SWE index lead is approximately four months prior to the monsoon. The yearly averaged Pacific SST index will have an averaged lead of six months on the monsoonal precipitation, meaning that SST index values recorded in each of the twelve months prior to the monsoon will be averaged annually into one value, which is to be correlated and regressed onto the monsoonal precipitation.

Any potential linkage between the monsoon and the Pacific SSTs will also be investigated because it is not clear, and even appears unlikely, that the snow depth anomalies are the driving force for the North American monsoon. Given the near proximity of the southwestern US and northwestern Mexico to the Pacific Ocean and the influence of the California Low-Level Jet, the Pacific SST anomalies such has ENSO and PDO may have an impact on moisture flux convergence overlying regions covering the equatorial Pacific northward into the northeastern Pacific. It is thus prudent to investigate the possible linkages between the three atmospheric and oceanic systems: North American monsoon, Pacific SSTs, and snow depth over the North American Rockies. If relationships are found between these three systems, it may be possible to find a driving force behind the North American monsoon via time leads and/or lags between each system. If such a driving force is found, it may also become possible to predict the monsoon and its variations ahead of time.

Data analysis includes the creation of indices of surface variables from the NARR data reanalysis, so that they could be correlated to each other as well as the Pacific SST indices calibrated for the time period of 1979-2002. To construct indices, the climatology and the anomalies (actual values minus climatology) of each field variable are computed. The indices are then standardized by dividing through the anomalies by one standard deviation. Before the standardization of these indices, areas with the highest variability are selected by displaying areas of highest standard deviation (> 0.5 mm/day for monsoonal precipitation) within the spatial domain. After the areas in the grid are selected, indices of area-averaged anomalies are constructed and again divided by one standard deviation. The area-averaged indices are then used for statistical analyses such as correlation and regression. Values of correlation between monsoonal precipitation and snow depth would be inter-compared with the correlations between the monsoonal precipitation and the ENSO & PDO indices. Correlations between indices and field variables, and linear regressions of indices on the field variables are computed to determine the linkages between snow depth, Pacific SSTs, and the monsoon. More variables, such as total columnar precipitable water (PWAT), zonal and meridional wind and specific humidity at 700 hPa and 850 hPa pressure levels, and moisture flux convergence, are also to be investigated to establish a more complete picture of the NAM.

A few potential problems may arise in the course of this project. One problem is the fact that monsoonal precipitation is convective in nature, with local enhancement via orographic effects, making accuracy difficult in precipitation measurements. Time lag is another factor that needs to be considered in this project, being due to the “memory” of the coupled atmosphere-ocean system. In this study, the time lead-lag for the SWE-monsoon relationship is approximately 4 months for SWE leading the monsoon. For the SST-monsoon relationship, the annually averaged SSTs use the previous 12 months before the start of the monsoon. The SST-SWE relation also uses the previous 12 months before each April, the month SWE data is used in this study. Another problem is with the quality of snow depth data and the fact that snow depth varies greatly over small spatial areas, such as the differences in snow depths on zonal windward slopes and lee slopes on an approximately north-south oriented mountain range. The snow data problem may be minimized by analyzing snow depth data at a fine resolution, as provided by the NARR reanalysis data. Although the snow water content within the snow may vary greatly with latitude and altitude, the snow water content is presumed to be about an order of magnitude less than the actual snow depths.

4.3 - Monsoonal Precipitation Climatology & Variability

The monsoonal precipitation climatology of the monsoon season, July, August, and September (JAS), shows that northwestern Mexico as well as southwestern US near the US-Mexico boarder east of the Gulf of California is very wet during the monsoon. At the far southern zones of the monsoon, the rainfall is on the order of over 4 mm/day, while further north into the US the rainfall is a less but nevertheless anomalously wet for a desert climate, about 1-2 mm/day. Monsoonal precipitation has a maximum of 4-5 mm/day on the east side of the Gulf of California that runs northwest from western Mexico into the far Southwest U.S. From Figure 2a, it may be noted that the nose of monsoonal precipitation surges northward from south of the US-Mexico border into Arizona and New Mexico from July into August. The heaviest precipitation remains in the southern monsoonal zones in northwestern Mexico. In August, some of the precipitation in excess of 1 mm/day surges into Arizona, New Mexico, up to the 39°N line, and then fades southward into September. Between 20°N and 30°N, precipitation remains nearly constant throughout the monsoon and abating slightly in September. However, the monsoonal precipitation that had extended northward into the US abates in September, while most of the moisture remains south of the US-Mexico border. Another climatological variable of importance, PWAT (Figure 2b), is the total column water, an integral of specific humidity from the surface to the tropopause. Total column precipitable water (PWAT) remains nearly constant throughout the monsoon, with a maximum of 40-50 kg m^-2 south of 30°N. The highest PWAT values are centered in the Gulf of California, where the SSTs are the warmest, much warmer than the open Pacific Ocean on the west side of Baja California. This assessment of monsoon precipitation agrees well with Ropelewski et al (2005), Higgins & Shi (2000), and several other studies. Their analysis showed that the monsoon rainy season lasts about 100 days, with August as the rainiest month and July with the most variability in precipitation due to changes in the onset date of the monsoon. Ropelewski et al (2005) have also suggested that there are several dynamical mechanisms that may modulate rainfall. These mechanisms may include but are not limited to pressure surges, easterly tropical waves, and variability associated with the Madden-Julian Oscillation (MJO). However, none of these mechanisms appear to explain most of the rainfall and its variability, and may be associated with transients rather than the mean flow.

Additional climatological variables besides just precipitation and PWAT are needed to establish a better picture of the North American Monsoon, especially moisture transport over the region during the monsoon (Figure 2c). At 700 hPa, there exists a southerly wind between 27°N and 40°N that flows from the northern Gulf of California well into the US. These winds flow from a region of maximum specific humidity (> 7 g kg^-1) to areas of lower humidity within the NAM region. This flow down the humidity gradient is much more pronounced in August, the height of the monsoon season, and abates slightly in September. However, in the low levels (850 hPa) there exists a low level California jet flowing southward from the northeast Pacific to the Baja California as a result from the circulation of the Pacific High and the land-sea temperature gradient. At the south end of the jet, the jet splits some of its flow, one branch turning anticyclonically to the west and another branch turning cyclonically towards Southwest US and Mexico. The flow towards the landmass acquires positive relative vorticity due to a surface thermal low centered over the California-Arizona-Nevada borders, and subsequently flows northward from the Gulf of California into the NAM region. At the low levels, there is an influx of relatively dry air from the Pacific into the Baja region and the NAM. This westerly flow of relatively dry air is presumed to push the humidity maximum from right over the Gulf of California eastward into the adjacent lands of northwestern Mexico. However, easterly flow from the Bermuda High keeps the moist air concentrated over northwestern Mexico and within the low level monsoonal jet that brings moist air into Southwest US. This convergence of moist air is referred to as moisture flux convergence (MFC). Because the NAM region is mountainous, much due needs to be given to the orographic effects on MFC and precipitation. This is supported by Figure 2d, a wide swath of positive (convergence) values are well inland, while the negative values lie immediately on the Gulf of California boundary where the influx of dry air from the Pacific Ocean begins to transport moisture inland. Further north into the Southwest US (zone #1), although the flow is nearly parallel to the humidity gradient, precipitation in the northern zones of the NAM may depend on the periodic bursts or quick surges of moisture that cannot be resolved on monthly or seasonal time scales. At the 700 hPa level and above, it is not clear where the moisture source lies. However, in the low levels, it is clear that the source of moisture for the monsoon lies in or near the Gulf of California, and perhaps to a lesser extent the Gulf of Mexico. But Ropelewski (2005) argues that the moisture gradients and winds in northern Mexico lend support to the view that some portion of the NAM precipitation may be fed by moisture from the Gulf of Mexico. The 700-hPa moisture and wind figures in this study lend some support for Ropelewski’s argument. It should be noted that a large area of the monsoon region have elevations above 2000 m, so any moisture transport from the Gulf of Mexico must occur above 800 hPa. The highest meridional water vapor fluxes lie along the Gulf of California and its eastern land boundary, northward into the Southwest US, with the maximum at where the Gulf of California terminates near the US-Mexico border. This falls in line with the wind and humidity profiles.

The variability of the monsoonal precipitation is shown in Figure 3a, where the values of the standard deviation are greater than or equal to 0.5 mm/day. The highest variability of precipitation lies in the designated south zone of the NAM, where standard deviation values run between 1.0 and 1.5 mm/day. Further north into the Southwest US (north zone), standard deviations are smaller at about 0.7 mm/day in some locations. Although the areas with the highest variability are to the south of the US-Mexico border, there is a comparative amount of variability north of the US-Mexico border given that these areas usually receive much less precipitation than the areas to the south. The northern zone of interest is enclosed by 33°N-36°N latitude and 118°W-113°W longitude, while the southern zone is enclosed by 26°N-32°N latitude and 113°W-109°W longitude. These zones are fixed throughout the JAS monsoon months. Another area with a notable standard deviation maximum is much further south, near the tip of the Baja California Peninsula. If transients are contributing to much of the precipitation variability, then the relative contributions of various transient phenomena such as Gulf surges, easterly waves, tropical storms, and MJO variability are still not clear (Ropelewski et al, 2005). The highest variability of PWAT (Figure 3b) in the NAM region is slightly outside and further west than the NAM zones arbitrarily determined by the precipitation standard deviations. Therefore the maximum standard deviation for PWAT is off-centered from the maximum standard deviations for precipitation. Despite this, it will be found that PWAT correlates strongly with precipitation. So on monthly and seasonal time scales, it is not clear why the PWAT variability maximum is off centered from the precipitation variability maximum. Perhaps this could be attributed to orographic effects, low level convergent flows, influx of dry air from the Pacific Ocean, moisture surges of much shorter duration than the monthly time scales used in this study, or a combination of all these. However, the specific humidity profiles shows that at the low levels, the maximum standard deviation of specific humidity do lie within the monsoon zones selected using the precipitation variability maximums for this study. Not surprisingly, this indicates that the humidity profiles at the low levels are of more importance than those at the 700 hPa or above. In the upper levels, higher than the 700 hPa, strong westerlies may bring relatively cool air aloft over the region, contributing to the destabilization of the atmosphere during bouts of strong surface heating. On the other hand, if the Pacific High and the Bermuda High are stronger than normal, these highs act together to stabilize the atmosphere and cut off thunderstorm activity by introducing a flow of drier air into the north zone of the NAM. Although, alternation between these bursts and breaks of the rainfall within this monsoon is beyond the scope of this research, it has much to do with the variability of winds during the monsoon season.

There is limited variability in both zonal and meridional winds in the NAM, on the order of a meter per second or less. In climatology, total wind speeds within the monsoon run around 3-6 m/s. This discourages applying the physical theory to the NAM that anomalous snow cover reduces the land-sea temperature gradient to weaken the Indian Monsoon to the mechanisms of the North American Monsoon. The land surface of Mexico, Arizona, New Mexico, Nevada, and the deserts of California all heat up rapidly to around 40°C. The Gulf of California SSTs soar to around 30°C, thus providing an ample moisture source via evaporative fluxes into the atmosphere. Despite the warmth of the Gulf of California SSTs, the land surfaces surrounding the gulf are even hotter so there is still a large land-sea temperature gradient. Consequently, specific humidity and moisture flux convergence having stronger variability than the winds adds significantly more weight to the idea that the precipitation resulting from the NAM varies slightly more with moisture than with the winds. The figure that displays the standard deviation of moisture flux convergence lends support to this idea because most moisture flux variability runs along and inland of the eastern boundary of the Gulf of California, also enhanced by orographic effects. There may be transient motion within the Gulf of California, where Gulf surges (pulses of southerly winds that transport moisture up the Gulf of California) of moisture may contribute to the variability of monsoonal rainfall, however even this may be debatable (Ropelewski et al, 2005). Although the above still does not indicate the exact sources of anomalous moisture, wind and humidity profiles show that it is unlikely that moisture from the Gulf of Mexico would cross the continental divide into the monsoon, except perhaps at around 700-hPa. There is no strong evidence for the dominance of any one transient phenomenon in producing NAM rainfall, and although there may not one dominant mechanism, each mechanism involved contributes to the rainfall and the relative contributions for any season is random (Ropelewski et al, 2005).

Figure 2a - Monsoonal Precipitation Climatology 1979-2002 for July, August, September (JAS) – Units in mm/day

Figure 2b - Monsoonal PWAT Climatology 1979-2002 for July, August, September (JAS) – Units in kg/m²

Figure 2c-i - Monsoonal Wind/Humidity Climatology 1979-2002 for July - Units in m/s for wind, g/kg for humidity

Figure2c-ii - Monsoonal Wind/Humidity Climatology 1979-2002 for August - Units in m/s for wind, g/kg for humidity

Figure 2c-iii - Monsoonal Wind/Humidity Climatology 1979-2002 for September - Units in m/s for wind, g/kg for humidity

Figure 2d - Moisture Flux Convergence Climatology 1979-2002 for September - Units in 10^-4 g/kg/s-1

Figure 3a - Monsoonal Precipitation Variability 1979-2002 for July, August, September (JAS) with fixed N & S Zones

Figure 3b - Monsoonal PWAT Variability 1979-2002 for July, August, September (JAS) with fixed N & S Zones

4.4 - SWE & Monsoon Correlations

The snow depth in the US Rockies area US1 has shown a marginally significant positive correlation with the monsoonal precipitation, especially in August and September. However, US2 has showed very little to no correlation to the monsoonal precipitation. As for the Canadian Rockies, here was a marginal negative correlation between the south zone of the monsoon and the snow depth in C2, especially in the midst of the monsoon season. However, this inverse relationship is non-existent near the beginning and ending of the monsoon season, raising questions about the consistency of the relationship between the monsoon and the remote Canadian Rockies. The results with C1 have also largely been inconsistent, and thus statistically insignificant. In the correlation table, Table 1, it can be inferred that there may be a relationship between the monsoon and the US & Canadian Rockies but is determined by external factors such as Pacific SSTs, meaning that the North American snow mass is unlikely the driver of the monsoon. The correlation values with the highest statistical significance (>95%) is during the month of August, the midst of the monsoon season.

July:	*US1*	*US2*	C1	C2
*North Zone*	0.29	0.07	0.10	0.06
*South Zone*	-0.03	0.09	0.16	-0.02
August:	*US1*	*US2*	C1	C2
*North Zone*	0.55	0.05	0.03	-0.25
*South Zone*	0.40	0.17	-0.20	-0.34

September:	*US1*	*US2*	C1	C2
*North Zone*	0.23	0.10	0.19	-0.13
*South Zone*	0.25	-0.18	-0.05	0.10

Table 1 - Correlation between Snow Depth (SWE) & Monsoonal Precipitation. Values that are grayed out have statistical significance of less than 95%.

These contradictory results seem to coincide with those of much research that had been done on the Indian Monsoon - Eurasian/Himalayan Snow Cover relationship. However, the finding of reversed relationships between the monsoon and the US & Canadian Rockies and the spotty statistical significance of these correlation values raises questions of what actually drives the monsoon, and whether its effects on the US Rockies are reversed for the Canadian Rockies. In an attempt to answer these questions about the monsoon, the linkage of the ENSO index and the Pacific Decadal Oscillation with the monsoon has been investigated.

4.5 - Relationship between Pacific SSTs & SWE

Since the index dates much further back from 1979, monthly index data from April 1978 to April 2002 and all the months in between was spliced from the PDO index. The spliced index was recalibrated by computing the average value from April 1978 to April 2002 and then subtracting this average value from the actual values of the spliced index. The ENSO-3.4 index has been extracted from the NARR data, and both indices are shown in Figure 4. The annual averaging procedure described in section 3 has been applied to both indices that date from August 1978 to August 2002 to ensure the same lead-lag times for the monsoon since the monsoon season gets well underway approximately four months after April, the month when the SWE data is of interest. Since the ENSO and PDO vary on interannual and decadal time scales, respectively, a four month difference in annual values between April and August of the same years is found to be negligible.

Figure 4 – ENSO/NINO-3.4 Time Series (left) & PDO Time Series (right): Each from April 1978 to April 2002

The simultaneous correlation between the ENSO-3.4 and PDO time series is marginally positive (r = 0.34). However, the ENSO and PDO have distinctive spatial (equatorial and mid-latitude, respectively) and temporal (interannual and decadal, respectively) features that differentiate one from the other. To elucidate these linkages between the Pacific SSTs and the April SWE, annual averages of Pacific SSTs were taken in such a way that all the values from the previous twelve months are averaged, where the twelfth month coincides with the SWE data (i.e. April). This procedure is repeated for subsequent years until April 2002. Regressions between the Pacific SSTs and annually averaged April SWE (not shown).

As shown in Figure 5, many similarities exist between the influence of ENSO and PDO on snow accumulation in the North American Rockies. Correlation analysis shows that both ENSO and PDO correlate positively with the SWE anomalies within the realm of the US Rockies. However, the reverse is true for the Canadian Rockies. Positive ENSO and PDO events are associated with anomalously low SWE in the Canadian Rockies, except for some local spots. Regression analysis shows that positive ENSO events are associated with above normal snow depth in US1. For the Canadian Rockies, below normal snow depth for both C1 and C2 are associated with either a positive ENSO or PDO. The ENSO and PDO have shown to have an equal amount of influence on SWE anomalies for much of the Canadian Rockies. However, the PDO has shown little or no effect on the SWE anomalies in the US Rockies. The reversal of correlation and the sign of regression values from the US Rockies to the Canadian Rockies, especially in the ENSO regression, offer an important clue as to why the correlation results in Table 1 show a similar reversal in sign from the US to the Canadian Rockies. Before drawing further conclusion from these results, the linkages between the Pacific SSTs and monsoonal precipitation are to be discussed next.

4.6 - Relationship between Pacific SSTs & North American Monsoon

Since the ENSO and PDO time series from 1978-2002 positively correlate, it is predicted that they both would have similar linkages with the North American Monsoon. In July, when the monsoonal precipitation is just beginning to occur in the southern zones, there is very little correlation between the precipitation and PDO indices. However, the ENSO 3.4 index and the July monsoonal precipitation are actually slightly anti-correlated. However, once the monsoon is well underway into August, the linkages between the Pacific SST indices and the precipitation become much stronger. The anti-correlation between the ENSO and monsoonal precipitation entirely vanishes as the monsoon season progresses from July into August. Some local areas in both the north and south zones of the monsoon have positive correlations exceeding 0.5 in the case of ENSO and PDO events, particularly near the Baja California Peninsula. The correlations between the PDO and the monsoon also show a change from July to August similar to ENSO. Into September, although the monsoon begins to abate, there are still marginally significant correlations between both Pacific SST indices and the monsoonal precipitation. ENSO correlations show a surge in positive correlations much further north than the north zone of the monsoon, however the PDO correlations does not show this northward surge. With the exception of July, the antecedent annually averaged August ENSO and PDO indices are positively correlated with the monsoonal precipitation in both the northern and southern zones, with the strongest linkage during August. At the height of the monsoon season, the correlations for Pacific SSTs and monsoonal precipitation are very high further south from the areas of interest, along the southern tip of the Baja California Peninsula. The regression analysis between the Pacific SST indices and the monsoonal precipitation has showed remarkable results. In Figure 7a, only the far southern zones of the monsoon are shown to be wetter than climatology in the event of either a positive ENSO or a positive PDO episode. Into August however, moisture surges northward well into southwest US, which is a remarkable change from only a month previous. A comparison between Figure 7a and 7b shows how much difference one month makes when the monsoon season gets underway, and how the Pacific SST anomalies may be used as an aid to predict the strength of the monsoon into August and September. Into September the monsoon abates slightly, but Figure 7c shows that the ENSO signal is still strong in the northern zones of the monsoon well into the southwest US. While the ENSO signal remains strong through September, the PDO signal is much weaker and less intense especially in the northern zones. For each month, regression values show that the ENSO and PDO both have similar amplitude of signals in monsoonal precipitation, as the precipitation maxima in the both regressions is about 0.5 mm/day. Past studies have investigated the influence of ENSO on NAM rainfall, and it was found that there are correlations between seasonal monsoon rainfall and ENSO (Ropelewski et al, 2005), as well as intraseasonal variability such as a dry July preceding a wet August and September. Higgins and Shi (2000) also found that warm PDO episodes during the winter through spring precede monsoons with early onset dates and a wet July, and the opposite (late onset, dry July) is true for cold PDO events. The PDO regression in Figure 7a agrees remarkably well with the assessment made by Higgins and Shi. On the flip side, the ENSO regression in Figure 7a shows that a warm ENSO event precedes a monsoon with a late onset date and a dry July, which also agrees with the conclusions made by Higgins and Shi (2000).

FIGURE 7 NOT AVAILABLE AT THIS TIME

To gain a deeper understanding of the NAM beyond the effect of Pacific SSTs on monsoonal precipitation, more variables such as total columnar precipitable water (PWAT), moisture flux convergence (MFC), and wind velocities were investigated using similar procedures outlined in section 3. During the monsoon, PWAT anomalies are strongly correlated with monsoonal precipitation (r = 0.7 for zone #1, r = 0.8 for zone #2) near the areas of highest variability in precipitation. Zonal wind velocities at the low levels (850-700 hPa) are anti-correlated with monsoonal precipitation; -0.6 for zone #1, -0.75 for zone #2. Meridional wind velocities at the same levels of interest are also anti-correlated with monsoonal precipitation on the west edge of the NAM region, and correlated with monsoonal precipitation on the east side of the NAM. The shape of these meridional wind correlations appears to outline the monsoonal low-level jet (strongest at 700 hPa) in a swath between 110°W and 105°W, flowing northward from 20°N to 36°N, with the largest positive correlations at 0.4 for zone #1 and 0.6 for zone #2. These aforementioned wind correlations are the strongest and more uniform between 700 hPa and 850 hPa, presumably because these winds flow relatively uninterrupted over the mountains of the NAM region. However, wind correlations are not consistent for September. The only correlations that are consistent and statistically significant from month to month through the entire duration of the monsoon are between PWAT and precipitation.

For precipitation anomalies of amplitude of at least one standard deviation (about 0.7 mm/day), there would be positive PWAT anomalies on the order of 1-3 kg m^-2, which is approximately less than one standard deviation of PWAT anomalies. For zone #2, the maximum PWAT anomalies are off slightly to the west of the designated zone. At 850-700 hPa, there would be negative zonal wind anomalies of about 0.2 to 0.8 m s^-1 (weaker zonal flow) which is less than one-half to one standard deviation in most locations. Therefore, the circulation around the thermal low at 700 hPa is on the order of 0.5 m/s (one-half standard deviation) stronger to produce one standard deviation of precipitation, as indicated by a swath of stronger meridional wind velocities in Figure 9c. For moisture flux convergence (not shown), there exist convergent values up to 5 x 10^-5 g kg^-1 s^-1 along and inland of the Gulf of California in July and August, and then become much smaller in September.

Regressions between the wind and moisture variables and the Pacific SSTs were also produced. The regressions between MFC and the Pacific SSTs (both ENSO and PDO) are chaotic for all months, which is a sign that MFC is primarily induced by orographic effects in mountainous terrain rather than any large scale convergent flows forced by the ENSO. In the month of July, regressions between precipitation and Pacific SSTs showed negative anomalies of 0.2-0.5 mm/day for a warm ENSO event, as shown in Figure 7a. However, these anomalies flip signs and become positive through August and September (Figure 7b-7c), an odd pattern that has become familiar in this study. Similarly, PWAT regressions show negative anomalies up to 2.5 kg m^-2 for a warm ENSO event, but anomalies become positive through August and September (not shown). During a warm ENSO event, the low level atmosphere within the NAM region may initially be anomalously dry, but quickly becoming anomalously wetter as the monsoon progresses. Also for a warm ENSO event, positive zonal wind anomalies (not shown) of about 1 m s^-1 appear at 700 hPa in July, then zonal wind anomalies become neutral to weak negative after July. In addition, there is little or no effect by the ENSO on meridional wind anomalies, which are relatively small in amplitude. Oddly, the flip from dry to wet conditions showed in the ENSO regressions were not present in the PDO regressions, which showed positive precipitation anomalies up to 0.5 mm/day for all three months (Figure 7). PDO and PWAT regressions show a similar picture; the wetness is confined to the south zones in July and spreading northward into the US thereafter. Interestingly, the PWAT regression in August shows a particularly wetter signal from a warm PDO event than a warm ENSO event.

What basically drives a monsoon circulation is the land-sea thermal gradient. The land, especially the desert areas of the Southwest US and northwestern Mexico, has a much smaller heat capacity than the Pacific Ocean and Gulf of Mexico. Consequently, the land heats up much more rapidly than the neighboring seas. The warming of the land relative to the ocean leads to enhanced cumulus convection, and hence to latent heat release, which produces warm temperatures throughout the troposphere (Holton, 2004). With larger warming over land, the tropospheric thicknesses are larger over the land than the ocean. The difference in thicknesses gives rise to a pressure gradient force directed from the land to the ocean at the upper levels. This pressure gradient force drives a divergent wind, which causes a net mass transport out of the atmospheric column above the landmass. This outward transport of air generates a surface thermal low over the landmass. In response to this surface thermal cyclone, a low level convergent wind develops, which produces moisture convergence making the environment more favorable for development of cumulus convection. Subsequently, this cumulus convection becomes the primary energy source for this monsoonal circulation. The lack of consistent correlation between zonal or meridional flow and the monsoonal precipitation shows that monsoons may still occur in a dry atmosphere, albeit with less eddy potential energy (Holton, 2004). Eddy potential energy in a monsoon is generated by diabatic (latent and radiative) heating, which does not involve the zonal mean energy. Rather, the eddy potential energy is converted to eddy kinetic energy by a thermally direct secondary circulation while the eddy kinetic energy is frictionally dissipated (Holton, 2004). The presence of cumulus convection and its latent heat release amplifies this eddy potential energy generation. Therefore, the variability of precipitation resulting from the NAM does not lie in the variability of the monsoonal flow associated with the land-sea temperature gradient, but rather in the variability of thermodynamic variables such as moisture fluxes and the amount of precipitable water in the atmospheric column over the land mass. However, where and what are the exact sources of moisture for the NAM is still an open question. This somewhat disputes past studies that claimed to find evidence of a linkage between snow cover and the NAM, except perhaps those studies that focused only on the onset of the monsoon.

The US1 snow depth in the US Rockies shows a positive correlation with the North American Monsoon, particularly during August and September. Despite close proximity, the same cannot be said for US2 snow depth, also in the US Rockies, as the correlations are much more insignificant as well as inconsistent. Interestingly, there is marginally significant negative correlation between the North American Monsoon and the snow depth in the Canadian Rockies. The reason behind the negative correlation between the monsoon and Canadian SWE anomalies can be made clear by looking at the regression figures of the Pacific SST indices, namely ENSO and PDO, on Canadian Rockies SWE anomalies. The negative correlation between ENSO and the snow depth anomalies in Canada is not surprising due to the observed dryness through western Canada during a warm ENSO event; while the southern US Rockies become wetter due to a westerly jet through the southern US during a warm ENSO event. Pacific SST indices lead the SWE anomalies and the JAS monsoonal precipitation by one year of SST forcing. This may be an indication that the Pacific SSTs drive the monsoon via increased evaporation rates overlying anomalously warm SSTs, subsequently via increased moisture flux convergence into northwestern Mexico and southwest US. This may mean that any linkage between snow depth anomalies and the monsoon may be merely coincidental. Orographical effects may also be taken into account as forced vertical motion is proportional to the strength of upstream winds from sea to land. The correlation between the SWE anomalies of the Canadian Rockies and the JAS monsoonal precipitation is the opposite of the correlation between the SWE anomalies of the US Rockies and the JAS monsoonal precipitation. These seemingly contradictory results seem to coincide with those of research that had been done on the Indian Monsoon – Snow Cover relationship. However, the contradictory results reproduced in this study may be simply due to the opposite effects of the ENSO on the snowfall in the US Rockies and in the Canadian Rockies. As shown in the correlation and regression figures, the effect of Pacific SSTs on the US Rockies versus the Canadian Rockies appears to be opposite of each other. The US Rockies snow accumulations were above normal while the Canadian Rockies snow accumulations were below normal during warm ENSO/PDO events. Since the Pacific SST indices lead the both the SWE anomalies and the monsoonal precipitation, Pacific SST forcing is likely to be the driving mechanism for both snow accumulations over the US and Canadian Rockies as well as the rainfall over the North American Monsoon region. This is one way to explain the contradictory results between SWE anomalies and the monsoon; Pacific SSTs appears to be the factor that determines the coincidental linkage between the monsoon and snow anomalies. However it is still unclear on whether the SWE anomalies have any impact on the monsoon, if at all. For example, this study says nothing about the onset of the monsoon, of which the SWE anomalies may still influence via land-sea temperature gradients for a brief period of time.

ENSO has been mostly positive since the mid-late 1970s, and this may have skewed the results in this study because it is still unclear how a strong La Nina event affects the monsoon. The PDO also has mostly been positive since the 1970s, and has a much longer periodicity than the ENSO (15-30 years). When the PDO is in its warm phase, the tropical Pacific waters are also anomalously warm, hence the marginal positive correlation between the ENSO and PDO. While this is the case, the North Pacific waters are anomalously cool. This entails wet conditions in the central and southwest US, including the monsoon region, during the warm season. So while the warm PDO events usually are associated with anomalously wet conditions in the NAM, it is still not clear where and what the moisture sources are. The same is true for warm ENSO events, except that in the case of ENSO the monsoon has a late onset date resulting in an anomalously dry July, especially in the northern zones of the NAM. This problem is complicated by the fact that there is relatively little variability in the winds of the NAM and the circulation of the low level thermal cyclone during the monsoon season. This implies that NAM variability is locally forced by thermodynamic mechanisms and orographic effects, such as strong surface heating, advection of cool air aloft, atmospheric destabilization, inflow of moisture from the Gulf of California, and orographically forced convergent and vertical motions. That being said, any evidence that snow cover and snow depth has a large scale effect on the monsoon is very weak. To determine the sources of moisture and to fully understand the local forcing mechanisms of the monsoon, smaller spatial and time scales may be useful for future research of the NAM.

Even if the monsoonal flow does not change in strength from year to year, as shown by small standard deviations of wind anomalies, there would still be variability in monsoonal precipitation due to SST variations where the flow originates. Anomalously cool SSTs in the moisture sources of the monsoon decrease evaporation rates and thus the air overlying these cool anomalies would also be drier than climatology. As climatological flow advects this anomalously dry air into the monsoonal region, less precipitation would occur due to decreased moisture flux convergence, which in this case is a combination of decreased moisture advection and increased thermodynamic stability due to a local decrease of moisture. Conversely, when anomalously warm SSTs are present in the Pacific, evaporation rates increase. The same climatological flow then advects anomalously moist air into the monsoon region, increasing moisture flux convergence. Moisture advection, low level convergence, and thermodynamic instability would each increase as the monsoon begins. Due to the mountainous terrain of northwestern Mexico and southwest US, orographical effects would also enhance vertical motion and rainfall. From this study, there is potential for future research. Due to many questions raised, the ENSO-monsoon or PDO-monsoon relationship may be further investigated to determine if the Pacific SSTs are indeed the stronger factors in driving the monsoon. Otherwise, the exact moisture sources and which transients contribute the most to monsoon rainfall will need to be determined. The relationship between SWE and the monsoon may also be investigated on daily-weekly time scales to determine its influence on the onset of the monsoon.

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