Section 2. Flow Timing


Puget Sound river hydrology could be affected by climate change. Precipitation in the region occurs predominately in the winter months. The accumulation of snow in the mountains is a primary storage mechanism, particularly for the snowmelt-dominated and transitional river systems. It has been estimated that more than 70% of total stream discharge in the Western United States is from melting snowpack (1996). An estimated 27% of summer streamflow of the Nooksack River originates from high-elevation snowshed and glacier-derived meltwater (Bach 2002). Climate change assessments predict increased winter and spring temperatures, resulting in decreased snowpack storage in the mountains, increased winter runoff as more precipitation falls as rain, and lower summer flows (Hamlet and Lettenmaier 1999, Lettenmaier et al. 1999, Mote et al. 1999, Leung et al. 2004, Barnett et al. 2008). Climate change may force rivers with snowmelt-dominated and transitional hydrological flow patterns towards rainfall-dominated hydrology (Mote et al. 1999). These changes are measurable through flow timing metrics, including the timing of the center of mass of annual flow (CT).

Prediction of the regional impacts of climate change on river and stream hydrology can be confounded by typical variation in rainfall patterns, high geographic variability, and land use changes. At least two large-scale systems affect annual climate variations in the Pacific Northwest (Mote 2003). These are the El Niño/Southern Oscillation, with a period of 2 to 7 years, and the Pacific Decadal Oscillation (PDO), with an estimated period of 20 to 30 years. Warm and cool phases of the El Niño/Southern Oscillation and/or Pacific Decadal Oscillation can result in variations on the order of 1°C for temperature, and 20% for precipitation (Mote et al. 2003). Hamlet et al. (2005) utilized a Variable Infiltration Capacity model to discern long-term trends in spring snowpack and snowmelt timing, decadal temperature and precipitation variability. They found that the date on which 90% snowmelt occurred correlated strongly with winter temperatures in the Pacific Northwest, and that there was a long-term warming trend that was not associated with decadal oscillations. In a subsequent study, Hamlet et al. (2007) specifically investigated the relationship between temperature, precipitation, and runoff timing in the western United States and found that in warmer areas, including the Pacific Northwest, fractional streamflow tended to occur earlier in the year (Hamlet et al. 2007). Mote et al. (2008) concluded that the primary factor in decreasing snowpack in the Washington Cascades was rising temperatures, consistent with the global warming. The long-term snowpack trends were unrelated to the variability brought about by Pacific oscillations.

Stewart et al. (2004) investigated historical (1948-2000) and projected future streamflow timing in snowmelt dominated rivers and streams in the Western United States. They found significant trends towards earlier runoff in many rivers and streams in the Pacific Northwest. Utilizing a ‘business-as-usual’ emissions scenario with a Parallel Climate Model, they predicted a continuation of this trend, largely due to increased winter and spring temperatures, but not changes in precipitation. In a companion study they further analyzed the trends in streamflow timing with variations of the PDO (Stewart et al. 2005). While streamflow timing was partially controlled by the PDO, there remained a significant part of the variation in timing that was explained by a longer-term warming trend in spring temperatures. This suggests that earlier seasonal flows may be associated with warming.

In addition to accelerated spring snowmelt, the shift toward earlier runoff timing can be attributed to a larger fraction of winter precipitation occurring as rain instead of snow. Knowles et al.(2006) evaluated data from the western United States and found a decreasing fraction of winter precipitation falling as snow. The largest decreases occurred in warmer winter areas, such as the Pacific Northwest, where relatively small increases in temperature would result in the transition from snowfall to rainfall, resulting in less snowpack and earlier runoff timing (Knowles et al. 2006).

Using a multivariate analysis, Barnett et al. (2008) evaluated simultaneous changes in average winter temperature, snow pack, and runoff timing in the Western United States (including the Washington Cascades) for the period from 1950 – 1999. They found significant increasing trends in winter temperature, and decreasing trends in snow pack and runoff timing (indicating earlier snowmelt) and that this was mostly like driven by anthropogenic forcing (Barnett et al. 2008).

Recently, the Climate Impacts Group at the University of Washington performed The Washington Climate Change Impact Assessment. The assessment included analyses of hydrology and water resource management in which they utilized results from 20 global climate models and two emissions scenarios from the IPCC Special Report on Emissions Scenarios (A1B and B1) to evaluate projected changes in spring snowpack and runoff (Elsner et al. 2009). For the rivers in the Puget Sound basin they found a dramatic decrease in spring snowpack, with almost no April 1 snowpack by 2080. During that period, river hydrographs progressively changed from transition or snow-rain dominated to rain dominated patterns. There was little predicted change in annual precipitation.

The observed and predicted changes in river flow regime described above can affect water resource management in the Pacific Northwest where systems have been designed based on historical flow patterns (Lettenmaier et al. 1999, Milly et al. 2008). Wiley and Palmer(2008) utilized a three-stage modeling approach to evaluate the potential impacts of climate change on the Seattle water supply system. They found a decreasing annual system yield (the amount of water that can be reliably supplied by a system) largely due to earlier runoff and decreasing water storage in the mountain snowpack. Vano et al. (2009) expanded this analysis to include the Everett and Tacoma water systems. They found that altered flow regimes likely will reduce the reliability of all three systems, particularly in the face of increasing demand, and could affect ancillary operations such as flood control, power generation, and the augmentation of environmental flows.

Several measures of flow timing exist. One measure of river flow timing is centroid timing (CT), calculated by Stewart et al. (2005) and Elsner et al. (2009):

where: qi=daily flow and ti=number of days past the beginning of the water year.

The centroid of flow measure is relatively insensitive to false interannual variations, is easy to calculate, and allows for easy comparisons of basins (Stewart et al. 2004).

There are approximately 90 gauging stations overseen by the United States Geological Survey (USGS) in the Puget Sound basin that are located on unregulated reaches of rivers and streams, which may be suitable for the analysis of streamflow status and trends (USGS Water Center); a list is provided in Chapter 1 of this report. A complete analysis of all of the available data was not performed for the purposes of this report. However, data from at least one unregulated gauging station within each Water Resource Inventory Area (WRIA) was included where possible in order to coarsely approximate a regional scale.

Data from all available gauging stations on unregulated reaches in the Skagit River basin were included in this analysis in order to evaluate whether there existed any basin-wide correlations in the hydrologic indicators. Previous reports have combined streamflow data from several rivers to evaluate regional trends (PSP 2009). A strong correlation between stream and rivers within the same basin would indicate that this is a valid approach.


Centroid timing values were calculated using gauge data from 14 different locations on unregulated rivers within the Puget Sound basin, in order to evaluate the status and trends of streamflow timing within the region. The results are shown in Table 1. The Pearson’s Correlation Coefficients for the annual CT are shown in Table 2.

Table 1. Calculated centroid of flow timing (CT) and trends in CT for unregulated rivers and streams in the Puget Sound



Centroid of Annual Flow


Data Years

Annual Change



(change ≠ 0)

WRIA 1 – Nooksack





USGS 12213100




WRIA 3/4 – Upper-Lower Skagit and Samish




Lower Sauk

USGS 12189500




Upper Sauk

USGS 12186000





USGS 12175500





USGS 12178100





USGS 12201500





WRIA 5 - Stillaguamish





USGS 12167000




WRIA 7 –






USGS 12134500




WRIA 8 – Cedar/Sammamish





USGS 12114500




WRIA 10 – Puyallup/White





USGS 12092000




WRIA 11 - Nisqually





USGS 12082500




WRIA 13 - Deschutes




Lower Deschutes

USGS 12080010





Upper Deschutes

USGS 12079000




WRIA 16 – Skokomish/Dosewalips





USGS 12054000





1. Center of Flow is calculated by:


Table 2. Pearson's Correlation Coefficient for annual CT for rivers within WRIA 3/4.


Lower Sauk

Upper Sauk





Lower Sauk







Upper Sauk




























Note: All Peasrosn’s correlation coefficients are significantly different than 0.

There appears to be a relatively strong correlation for this particular metric in flows within the Skagit River basin (r>0.85). The correlation between the rivers in the Skagit River Basin and the Samish River is less robust (r<0.65).


Annual CT values were calculated for the water years with complete data sets for 14 gauge stations in the Puget Sound. The trend of CT versus time was determined using simple linear regression. The significance of the trends were determined by evaluating the probability that the slope of the trendline was significantly different than zero. Results are shown in Table 1. The rivers with significant trends (P<0.05; Lower Sauk, Upper Sauk, Newhalem, NF Stillaguamish, and Skykomish) all showed an annual decrease in flow timing indicating that peak flows occur earlier in the year (Table 1). There were no rivers with significant trends indicating later flows. Overall, the centroid of flow timing occurred from 1.5-4 days earlier per decade. Data from two of the three rainfall-dominated river systems (Samish and Deschutes) and the single snowmelt-dominated river (Thunder) indicated no significant change in streamflow timing (P>0.05; Table 1).


The analysis presented above was derived from data in the public domain. The values and trends for CT were calculated from average daily discharge data from USGS station located in the Puget Sound region (United States Geological Survey 2010b). The datasets include qualification codes indicating whether data are provisional or have been approved (United States Geological Survey 2010a). We avoided using provisional data in this analysis, and we omitted data from gauging stations for which advisory notes warning against unreliable data quality had been posted. Average daily discharge data for each water year (October 1 – September 30) were used to calculate the CT. The existence of trends was determined by evaluating the probability of the slope of the CT versus year, as determined through simple linear regression; trends were those with slope significantly different than zero (P<0.05).

Due to interannual variation, the selection of the beginning and ending years of streamflow data may affect the significance of the trend reported in Table 1 . Konrad et al. (2002) used both parametric and nonparametric tests and found a high likelihood of Type I errors when using 10-year streamflow records to evaluate long-term trends. In this evaluation we used a minimum record length of 37 years; the shortest record that resulted in a significant trend was 47 years.

The significance of the Pearson’s correlation coefficient was determined by calculating the probability that the correlation was different than zero based on the value of the correlation and the sample size. A significant correlation does not indicate a strong correlation.


Of the fourteen data sets analyzed, four showed significant decreasing trends, indicating flow timing earlier in the water year. The rate of timing change was from 1.5-4 days per decade. The other ten data sets showed no significant trends.

There was significant variation in the flow timing data sets. However, there was a strong correlation in CT between rivers within the Skagit River basin (Pearson’s r>0.85). The correlation between the CT of the Samish river and the rivers in the Skagit River basin was weaker (Pearson’s r<0.65).

The CT could be a useful indicator of hydrologic alteration. It allows the tracking of potential changes due to climate, allows comparison of trends across different river systems, and is of importance to water resources managers. It may be more valuable when combined with other indicators of hydrologic alteration to give a more complete picture of streamflow patterns.


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