Lunar tidal influence on inland river streamflow across the conterminous United States

Authors


Abstract

[1] We employ a comprehensive (1900–2009) stream discharge gauge database to analyze the tidal impacts on inland streams. Our analysis reveals a strong lunar phase signal in stream gauge time series across the conterminous United States such that the largest tidal impact on inland rivers is evident at or just after the quarter moon (halfway between full and new moons). As an explanation, we examine precipitation using the Historical Climate Network precipitation dataset. Verifying early studies’ results, we find an equivalent well-defined lunar phase relationship with precipitation such that the largest tidal impact on precipitation generally occurs just before the quarter moon. Our results imply that inland precipitation is influenced by lunar tides and forces the lagged runoff evident in stream gauges. The lunar-induced periodicities in the stream gauge network, evident far from ocean-induced tides, may also influence flooding, as well as water management and power generation.

1. Streamflow Tidal Variations

[2] Research on the lunar tidal oscillations for streams has strongly focused on near-coastal estuaries with the implied assumption that only streams, or portions of streams, close to coastal areas will experience strong, identifiable tidal activity. If tidal influence can be identified far from the ocean, the periodicities inherent in tidal forcing may aid in the forecasting of flooding as well as in water management and power generation issues. This supposition that only near-coastal streams demonstrate strong tidal responses can be tested through study of a comprehensive database of all stream gauges across the conterminous United States. The United States Geological Survey Surface-Water Data for the Nation [U.S. Geological Survey, 2001] includes daily values for 24,964 sites. This is the same type of data from which a study demonstrated a strong diurnal signal in streamflow for rivers in the western United States linked primarily to diurnal snowmelt [Lundquist and Cayan, 2002]. From this extensive streamflow dataset, we extracted daily values for streamflow in cubic meters per second across the conterminous United States for the length of their record. We limited the analysis to streamflow gauges classified as being inland river stream gauges, not tidal stream gauges, that is, these stations were not located at the estuary of a river and thereby not experiencing direct oceanic tidal forcing.

[3] From this long record across the conterminous United States, we standardized each station’s daily streamflow values to its computed long-term mean and standard deviation. We selected only stations in which at least thirty years of daily data from 1900 to 2009 exist, for a total of 10,994 stations in eighteen hydrological basins (Figure 1). We then calculated the lunar phase for each day coinciding with the streamflow record by determining the average angular difference between the apparent longitudes of the moon and sun for that day [e.g., Meeus, 1991]. The cycle of lunar-phase magnitudes varies over the lunar synodic cycle of 29.53 days. We subdivided the phase data into ten classes, hereafter termed lunar synodic decimals as denoted in previous research [Bradley et al., 1962; Brier and Bradley, 1964; Hanson et al., 1987]. The lunar synodic decimal advances about 0.03 per day. A ten-unit moving total of a distribution within successive classes, each 0.1 in width, therefore, equates roughly to a 3-day moving total [Bradley et al., 1962].

Figure 1.

The locations (black dots) of the 10,994 streamflow gauges in The United States Geological Survey Surface-Water Data for the Nation network used for analysis (each with at least 30 years of data from 1900 to 2009). The locations (white squares) of the 1218 stations in the United States Historical Climatology Network (U.S. HCN) reporting daily precipitation (1895–2008).

[4] Each standardized daily streamflow value was classified by the associated lunar synodic decimal value. The composited average result of all stations across the conterminous United States along with the associated standard deviation of the mean is shown in Figure 2. The interesting and unexpected result is that a clear tidal response is evident such that the biggest tidal impact on streamflow across the United States is evident during and just after the quarter moon (halfway between full and new moons). When harmonic analysis is applied to the lunar-categorized data, the variance explained by the second harmonic (a two-peak distribution over the course of a lunar month) is r2 = 0.5546 (p < 0.01). The total variance explained by the first and second harmonics is r2 = 0.8924 (p < 0.001).

Figure 2.

Composited average standardized daily streamflow value for 10,994 stations in eighteen hydrological basins (each with at least 30 years of data from 1900 to 2009) as classified by the associated lunar synodic decimal value (1 = class directly following new moon; full moon occurs between classes 5 and 6; 10 = class directly preceding the new moon). The error bars associated with one standard error of the mean are given for each decimal value.

[5] For the periods of maxima in Figure 2 (lunar synodic decimal classes 2,3,7,8 and 9) and minima (lunar synodic decimal classes 1,4,5,6, and 10), the means of the standardized streamflow values were compared via a two-sample t-test. Additionally, the significance of the coincidence between above median streamflow values and the maxima was determined through a 2 × 2 chi-square test for independence [Hollander and Wolfe, 1999]. The results from both tests were extremely significant with χ2 = 635.1 and a t-value of 29.6. As both these statistical tests require independence of observations (likely not the case for the streamflow data due to spatial autocorrelation) we also calculated two-sided pseudo-significance values through Monte Carlo techniques similar to Wolter et al. [1999] by performing the above tests 9,999 times, each with a random assignment of the ten lunar decimal classes. Significance was determined from these empirical probability density functions as (K + 1)/1000 where K is the number of random trials producing test statistics more extreme than those originating from the actual lunar synodic decimal class assignments. Five runs of the Monte Carlo experiments yielded pseudo p-values of 0.0466 to 0.0496 for the chi-square test and from 0.0390 to 0.0414 for the t-test suggesting that streamflow values for the United States are highest during and just after the quarter moon (halfway between full and new moons).

[6] The strength of the inland tidal influence on streamflow can be demonstrated visually (Figure 3) by showing the amount of variance (r2) explained by the second harmonic for the lunar synodic month. A large number (2590, or 23.6 percent of all stations) of inland USGS streamgauge stations—some as far inland as the upper Midwest—display explained variances by a second-order harmonic for the synodic month which are statistically significant at the 0.05 confidence level. This reflects a double-peaked cycle with maxima in both the period between new and full moons and the period between full and new moons. The question can immediately be raised as to why such a lunar phase signal is evident in inland streamflow data.

Figure 3.

Variance explained (r2) by the second harmonic for lunar month for the 10,994 stations in eighteen hydrological basins (each with at least 30 years of data from 1900 to 2009) of the USGS streamflow database. The size of the circle indicates the degree of significance such that the smallest circles indicate variances not significant at the 0.10 confidence level, the medium circles indicate variances significant at 0.10 confidence level and the largest circles indicate variances significant at the 0.05 confidence level.

2. Potential Causes

[7] Camuffo [2001] proposed that such a signal might be explained in that “in some cases the tidal oscillation of the underground water table may induce a variable supply of water …” However, we believe a more likely mechanism than water-table variability to account for lunar influence on discharge rates of streams across the conterminous United States may be the underlying basin-wide input of water into these streams from tidally-influenced precipitation.

[8] A number of older studies, primarily in the 1960s and 1970s, showed strong relationships between the lunar synodic cycle and precipitation. Bradley et al. [1962], using the daily histories of 1544 weather stations over a fifty-year period from 1900 to 1949, revealed that the greatest rain totals occur most frequently in the first and third weeks of the lunar synodical month, corresponding to the period just after the new moon and just after the full moon. Adderley and Brown [1962] extended Bradley et al.’s results and demonstrated that for fifty New Zealand stations for the years 1901–1925 a similar pattern of highest rainfall corresponding to just after new and full moons was evident. Lethbridge’s [1970] examination of 108 stations showed that greatest thunderstorm frequency for the period 1953 to 1963 occurred two days after full moon. Recently, Roy [2006] demonstrated that an increased occurrence of precipitation occurred a few days after the full moon for stations (1910–2000) in the interior of India.

[9] As a potential cause to these previous findings of tidal forcing’s influence on precipitation and thunderstorms, past climatological and astronomical research has proposed that the lunar synodic cycle may be linked to (a) lunar distortion of the Earth’s magnetic tail [Lethbridge, 1970, 1990], (b) the occurrence of cosmic rays [Markson, 1981], and (c) variations in meteoric dust [Adderley and Brown, 1962] acting as condensation nuclei, among other explanations.

3. Lunar-Influenced Precipitation

[10] For the current study, to update the original precipitation/tidal research from the 1960s and 1970s and thereby potentially determine if precipitation is a potential intermediate link between the lunar tidal forces and streamflow, we analyzed one of the best quality-controlled regional precipitation databases, the United States Historical Climatology Network (U.S. HCN), which consists of observations from the U.S. Cooperative Observer Network operated by NOAA's National Weather Surface (NWS). The HCN dataset contains daily precipitation time series for these stations that are distributed in a relatively uniform fashion across the conterminous United States (Figure 1). The HCN dataset, consisting of 1218 stations, is a subset of the much larger U.S. Cooperative Observing Network, stations having been chosen based upon their spatial coverage, record length, data completeness, and historical stability (i.e., the number of changes in location, instrumentation, and observing practice) (for specific details on the HCN dataset attributes see Karl and Williams [1987], Easterling et al. [1996a, 1996b], Vose et al. [2003], and Menne and Williams [2009]). In short, HCN consists of among the highest-quality stations in the U.S. historical climate record. The HCN dataset has been developed at NOAA's National Climatic Data Center (NCDC) in collaboration with the U.S. Department of Energy's Carbon Dioxide Information Analysis Center (CDIAC) [Easterling et al., 1996b].

[11] To determine the tidal impact on the precipitation from the HCN data network, we employed the same data technique as used on the streamflow data. First, we extracted daily precipitation values from 1218 stations across the conterminous United States for the length of their record (extending from 1895 to 2008). From this long record for each precipitation value, we standardized the daily precipitation values of each station to the computed long-term mean and standard deviation of each station. We then calculated the lunar phase for each day coinciding with the precipitation record by determining the average angular difference between the apparent longitudes of the moon and sun for that day [e.g., Meeus, 1991].

[12] Not surprisingly, the synodic precipitation distribution from the HCN precipitation dataset is quite similar to that of previous studies from the 1960s and 1970s (Figure 4). Similar to the work by Bradley et al. [1962] and Lethbridge [1970], we show that the peaks in precipitation occurrence for the aggregated composite of all precipitation stations across the conterminous United States occurs between the new moon and the first quarter moon and between the full moon and the last quarter moon (Figure 4). When harmonic analysis is applied to the lunar-categorized data, the variance explained by the second harmonic is 0.4106 (p < 0.03). In addition, the phase angle of the second harmonic for the HCN precipitation data (time of first maximum: 4.04 days after the new moon) slightly precedes the streamflow data (time of first maximum: 7.41 days after new moon). This is likely the result of the time required for the runoff precipitation over the hydrologic basin to contribute to the streamflow of the given river. It should be noted that these lag times discussed above are averages for the all stations and the lagged response for individual stations may vary. As with the streamflow data, the amplitude of the first peak (between the new and full moons) is higher than the second peak (between the full and new moons).

Figure 4.

Composited average standardized daily precipitation value for 1218 stations in the United States Historical Climatology Network (U.S. HCN) (extending from 1895 to 2008) as classified by the associated lunar synodic decimal value (1 = class directly following new moon; full moon occurs between classes 5 and 6; 10 = class directly preceding the new moon). The error bars associated with one standard error of the mean are given for each decimal value.

[13] The strength of the inland tidal influence on precipitation can be demonstrated visually (Figure 5) by showing the amount of variance (r2) explained by the second harmonic for the lunar synodic month. A large number (281, or 23.1 percent of all stations) of HCN precipitation stations—again some as far inland as the upper Midwest—display explained variances by a second-order harmonic for the synodic month period which are statistically significant at the 0.05 confidence level. This reflects a double-peaked cycle with maxima in both the period between new and full moons and the period between full and new moons, generally lagging the maxima for streamflow.

Figure 5.

Variance explained (r2) by the second harmonic for lunar month for the 1218 stations in the United States Historical Climatology Network (U.S. HCN) (extending from 1895 to 2008). The size of the circle indicates the degree of significance such that the smallest circles indicate variances not significant at the 0.10 confidence level, the medium circles indicate variances significant at 0.10 confidence level and the largest circles indicate variances significant at the 0.05 confidence level.

4. Conclusions

[14] In conclusion, the aggregated streamflow data for the conterminous United States demonstrates a surprising and marked 29.53-day tidal signal with the highest discharge rates occurring during and after the quarter moon (halfway between full and new moons). While other factors (e.g., tidal oscillation of the underground water table) may also influence the marked tidal signal in inland stream discharges rates, our research indicates that a probable explanation for the marked tidal signal is the equally strong tidal influence evident in precipitation data noted by previous researchers and re-verified by this research using a high-quality precipitation dataset for the conterminous United States.

[15] This lunar synodic-influenced precipitation effect on inland stream discharge suggests an important corollary to human activity and safety. If, as we statistically demonstrate in this research, lunar tidal forcing exerts a definable influence on inland streamflow, then the inherent periodicities of tidal activity (∼29 days) may aid forecasters in predicting inland flooding as well as aid in power generation and water management issues.

Acknowledgments

[16] We thank Marco Marani and an anonymous reviewer for valuable comments. This research was funded in part through NSF grant 0751790.