By analysis of a unique and extensive photographic and written record spanning several decades, we characterized the spatial and temporal scales of morphological adjustment of the inlet of the Russian River Estuary, on the California coast. We paired this record with in situ measurements of beach features to create a dataset consisting of daily values of inlet width, length, shape, and position for the period of 1991–2006. Available wave, tide, and river flow data were compared with these measurements. We show that the spatial and temporal scales associated with adjustments in inlet geometry and position are dictated by different mechanisms during periods of high and low river flow and also vary with periods of large-scale climate oscillations. Our analysis of inlet shape reveals that several classes of inlet curvature correspond to unique flow, geometry, and risk of closure conditions.
 Coastal inlets regulate tidal conveyance in a variety of systems ranging from small tidal lagoons with no freshwater inflow to estuaries at the terminus of significant rivers [Shuttleworth et al., 2005; Kraus et al., 2008]. The importance of these systems stems from their association with unique ecological environments [Gladstone et al., 2006] and harbors of economic relevance [Escoffier and Walton, 1979]. While many coastal inlet systems maintain a state of morphologic equilibrium and vary little in position and geometry with time, inlets which migrate or experience seasonal or sporadic closure occur in virtually every arid and semiarid region of the world [Ranasinghe and Pattiaratchi, 2003]. Inlet migration [Galvin, 1971; Aubrey and Speer, 1984] and closure [Bruun and Gerritsen, 1960; Escoffier and Walton, 1979; Ranasinghe and Pattiaratchi, 2003] have received much attention in the last half-century. However, both the short- and long-term dynamics of coastal inlets still remain poorly understood [Goodwin, 1996]. Attempting to understand how these systems react to climate change will be difficult without a strong understanding of the mechanisms involved, and the level of inlet variability ascribed to climate change versus alternate sources of variability.
 The scientific goal of this study is to identify consistent behavioral patterns of coastal inlets with significant seasonal river influence at various time and length scales; in particular, inlet migration, shape, width, length and closure frequency. We aim to connect short- and long-term manifestations of these behaviors to climate patterns ranging from short-term changes in wave, tide, and river conditions to large-scale changes associated with El Niño-Southern Oscillation (ENSO) events. Knowledge of these connections will allow further research into the effects of sea level rise and changing wave and precipitation conditions on behavioral patterns of this and other river mouth systems around the world.
2. Data and Methods
 To achieve our goals, we compare gradients in observed parameters of a typical migrating Northern California inlet with gradients in available wave, tide, and river flow data. Closure frequency is obtained through written observations of the inlet condition over many years, while daily inlet position and geometry are determined by combining ground-level photographs of the inlet with known distances between landmarks on the beach. We compare inlet width adjustments with daily and seasonal changes in river flow and tide range to identify which processes control inlet geometry at different times of the year. We determine controlling factors in migration behavior by statistically analyzing individual migration events and by correlating annual migration patterns with large-scale Pacific climate oscillations. Finally, we distinguish different inlet shapes by their geometric features, flow characteristics, and risk of closure.
 We take as a study site the Russian River Estuary, located on California's Sonoma Coast (Figure 1). This site is representative of a family of rivermouths in semiarid climates which close either seasonally or sporadically during months of the year with low rainfall. Rainfall during the months from October to April provides the majority of the flow in the river, with discharges ranging from less than 5 m3/s during the summer months to more than 2500 m3/s during floods. Waves are predominantly from the northwest with periods from 12 to 16 seconds; significant wave heights for both sea and swell are highest from November to January [Rice, 1974]. Tides reach a maximum range of 2.7 meters, but the basin topography restricts the tidal prism to a smaller size than that of many other California estuaries [Goodwin and Cuffe, 1993].
 The migration of the mouth of the river was observed by the fourth author on a daily basis for 33 years from 1973 to 2006 (period 1984–2006 presented in Figure 2). Observations include written accounts of opening and closure events, as well as a daily set of photographs of the inlet from 1991 to 2006 (Figure S1 of the auxiliary material). This greatly exceeds typical data on inlet variability, in temporal resolution, duration and detail of observations. From this we created a database of morphological parameters for the inlet.
 To quantify inlet geometry and position from the photographs, we identified the range of inlet migration on the barrier beach and measured the distances between several large beach objects within this range. These objects include a jetty at the southern limit of migration, a rock escarpment at the northern limit, and a large boulder located roughly in the middle of the migration range (see Figure 1). These objects are also clearly visible in aerial photography of the estuary. The dimensions of the objects and the distances between them were measured in situ. The width and length of the inlet were visually estimated from each of the photographs through comparisons with the measured distances between the objects (see images in Figure S1). With this approach we also determined the location of the inlet by quantifying the distance north of the southern boundary of migration. We noted the degree of curvature and the number of arcs of the inlet for each day, and this classification is displayed in Figure S2. We chose to make estimates using this method because photographs were taken from an observer, rather than an automated device, and therefore they could not be orthorectified since they were taken from slightly different positions and angles each day.
 To validate our approach, we compared estimates of inlet width, length and position made from photographs with in situ measurements on several days during the years 2007 and 2008. We found that the average error of estimates was below seven percent for both the inlet width and length, as shown in Tables S1 and S2. Estimates of inlet location were within an eight percent error range, as shown in Table S3.
 We acquired wave and tide measurements from the Coastal Data Information Program (CDIP) Cordell Bank buoy, 39 miles southwest of the Russian River mouth (http://cdip.ucsd.edu/?nav=historic&sub=data&stn=029&stream=p1). A transformation matrix provided by CDIP was used to account for the effects of wave refraction between the buoy and the 50 m isobath offshore of the inlet. River discharge measurements were available from the archives of the California Department of Water Resources at a location 11 miles upstream from the rivermouth (http://cdec.water.ca.gov/cgi-progs/staMeta?station_id=HAC). Contributions from streams in the lower estuary were neglected because measurements from the U.S. Geological Survey showed that they account for less than ten percent of Russian River flow and vary in concert with flows in the Russian River. For considerations of large-scale climate oscillations, we obtained monthly records of the Multivariate El Niño - Southern Oscillation Index (MEI) from the National Oceanic and Atmospheric Administration (NOAA) (http://www.cdc.noaa.gov/people/klaus.wolter/MEI/table.html).
3. Results and Discussion
 Inlet closure (shown in Figures S1 and S3) typically results from the inability of the current in the inlet to erode and remove sediment being deposited in the inlet channel, a condition caused by weakening river flows, an inadequate tidal prism, an increase in frictional losses in the inlet channel [Elwany et al., 1998], or by an increase in the rate of sediment deposition [Shuttleworth et al., 2005]. We found that closures normally occur during periods of high waves and low tide ranges, with waves playing the dominant role. The combination of the small tidal prism, highly-variable wave climate and seasonally low river flow results in as many as 15 closures of the Russian River inlet each year, with a weak seasonal pattern in occurrence (Figure 2). Years shown by Figure 2 to have relatively high amounts of closure correspond to prolonged dry periods. Artificial breaching prevents closure periods from lasting more than two weeks. However, closure periods are in some cases abruptly ended naturally by storm events (about 30% of breaches) which can increase river inflow by a factor of ten or more in a couple of days, causing the estuary to rapidly overtop the barrier beach. A seasonal increase in wave heights, coupled with sporadic rainfall events and artificial breaching activity, often leads to a series of inlet opening and closure events during October–November.
 We found that three inlet shapes explain the basic features of the river mouth throughout the year. Table 1 shows that straight (no channel bends), curved (one channel bend) and meandering (multiple channel bends) inlets are each associated with a specific width, length, average river flow, and closure risk. We define closure risk as the ratio of two sums. The numerator is the sum of all days for which the inlet was classified as a particular shape within two weeks prior to a closure event. The denominator is the sum of all days for which the inlet was classified as that shape. We found that straight inlets have the shortest lengths, greatest widths, and are associated with high discharges and the lowest closure risk. Lower discharge, smaller width and greater length are associated with higher degrees of curvature. When discharge decreases to typical May–October values of less than 30 m3/s, the wetted cross-section decreases to accommodate the lower flow, often leading to a smaller inlet width. Concurrently, the weaker river flow allows waves to deposit larger amounts of sediment in the rivermouth. The deposited sediment often accumulates on one side of the mouth, and the river erodes the opposite bank to maintain its flow to the ocean, deflecting the mouth and causing it to migrate away from the source of sediment [Dean and Dalrymple, 2002]. The channel of the inlet follows the motion of the rivermouth, greatly increasing the inlet length (and flow bottom resistance effects) over time. When this results in a meandering state, the increased frictional loss of the elongated, winding inlet leads to a much higher risk of closure.
Table 1. Characteristics Corresponding to Different Inlet Shapes
Fraction of Recorded Days Characterized by This Shape
Error estimates are based on rounded results of Tables S1 and S2.
We define closure risk for each inlet shape as the fraction of total days in which the inlet is classified as that particular shape within two weeks of a closure event.
40 ± 3
75 ± 4
25 ± 2
145 ± 9
15 ± 1
200 ± 12
 Our analysis of inlet position revealed two dominant patterns of migration. In years showing the first pattern, the inlet migrates more than 100 meters north between the months of November and January, retraces the entire distance moving southward within several months, and undergoes smaller ranges of migration during the summer. Water years 1999–2000 and 2003–2004, shown in Figure 3, illustrate this pattern. This behavior characterized the period 1995–2006 except for the water year 1997–1998 (see Figure S4). The years 1991–1994 and 1997–1998 followed a markedly different pattern characterized by a similar migration northward between the months of November and January, but a much slower return southward, in some cases leaving the inlet near the northern boundary of migration for much of the summer. The water year 1992–1993, also shown in Figure 3, provides an example of this behavior. We found that all years characterized by the second pattern coincided with El Niño events for which the yearly-averaged MEI values exceeded a value of approximately 0.7. While the northward movement of the mouth during winter is consistent with greater river flow and the northwestward momentum of this flow, the reason for the lack of southward migration in El Niño years is not clear, although it is conceivably due to the absence of northerly winds and wind-driven waves in these years. In addition to inter-annual differences in mouth position, there are marked differences in the migration of the mouth when open. During the wet months (large river flow), the mouth migrates up to 250 m and does so over two or three months, while in the dry season the mouth typically migrates no more than 100 m and returns to the nearest boundary every few weeks (Figure 3).
 The roles of waves and river flow in influencing rivermouth migration events were investigated statistically by identifying dates of high discharge and wave height gradients and comparing those gradients with the rate of inlet migration. We selected thresholds for gradients in discharge (80 m3/s/day) and significant wave height (0.5 m/day). These thresholds were based on the distribution of values for each parameter. As summarized in Figure S5, we found that: (1) Hs gradients of at least 0.5 m per day preceded approximately 75 percent of all inlet migration events, and (2) The influence of riverflow increased with increasing migration rates, with 45 percent of events characterized by an average movement of 15 m/day preceded by a riverflow gradient of at least 80 m3/s per day. This analysis confirms that waves play a dominant role in inlet movement, but also shows that flood events can be tied to some of the most rapid changes in inlet position.
 Our analysis of the data shows that the inlet width follows recurrent seasonal patterns that are governed by river inflow. The wetter months of the year 2003 are illustrated in Figure 4 (top), with the width responding to discharge events. During summer, discharge decreases significantly, and inlet width responds to tidal fluctuations (Figure 4, bottom). Greatest widths during dry months are observed during spring tides, suggesting that the highest tide ranges provide enough flux through the inlet to significantly increase the width. The data suggest that the inlet width adjusts to the dominant process (in terms of flow rate) during a given period. In wetter months, inlet widths range from 50 to 250 meters, while the time scale of adjustment is on the order of several weeks, corresponding to the period between peak flow events. When the river only supplies minimal flow to the estuary, spatial adjustment scales to approximately 30 meters, and the temporal scale of adjustment corresponds to the periods between spring tide ranges.
 From an analysis of an extensive ground photographic record, we found that inlets with the greatest degree of curvature had the greatest length, smallest width, and the highest risk of closure occurring within two weeks. Our results also imply that adjustments in the geometry and position of a coastal inlet with river influence correspond to temporal and spatial scales which are dictated by the state of the river. For instance, the dominant morphological period during the wet season is the period between storm events, whereas the dominant period during drier months is the period between peak tides. Increases in wave height were found to be the most common precursor of rivermouth migration, although similar increases in river flow also had an influence prior to the fastest migrations. Two main modes of migration were identified, conceivably corresponding to El Niño variability. This strongly suggests that the migration of coastal inlets is influenced by large-scale climate oscillations. Finally, our results imply that periods of high river flow in these systems correspond to profound and relatively long-lasting adjustments, while periods of low river flow are tied to smaller and more rhythmic adjustments influenced by tides.
 Thanks to David H. Schoellhamer, University of California, Davis, Department of Civil and Environmental Engineering; Gregory B. Pasternack, University of California, Davis, Department of Land, Air, and Water Resources; Nick Kraus, United States Army Corps of Engineers, Coastal Inlet Research Program; Don Danmeier, Philip Williams and Associates Ltd. This study was partially supported by a research fellowship from the Bodega Marine Laboratory.