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Abstract

  1. Top of page
  2. Abstract
  3. Introduction
  4. The study area and data
  5. Spatial statistical analysis
  6. Results
  7. Discussion
  8. Acknowledgements
  9. References

Summer streamflow is a vital water resource for municipal and domestic water supplies, irrigation, salmonid habitat, recreation, and water-related ecosystem services in the Pacific Northwest (PNW) in the United States. This study detects significant negative trends in September absolute streamflow in a majority of 68 stream-gauging stations located on unregulated streams in the PNW from 1958 to 2008. The proportion of March streamflow to annual streamflow increases in most stations over 1,000 m elevation, with a baseflow index of less than 50, while absolute March streamflow does not increase in most stations. The declining trends of September absolute streamflow are strongly associated with seven-day low flow, January–March maximum temperature trends, and the size of the basin (19–7,260 km2), while the increasing trends of the fraction of March streamflow are associated with elevation, April 1 snow water equivalent, March precipitation, center timing of streamflow, and October–December minimum temperature trends. Compared with ordinary least squares (OLS) estimated regression models, spatial error regression and geographically weighted regression (GWR) models effectively remove spatial autocorrelation in residuals. The GWR model results show spatial gradients of local R 2 values with consistently higher local R 2 values in the northern Cascades. This finding illustrates that different hydrologic landscape factors, such as geology and seasonal distribution of precipitation, also influence streamflow trends in the PNW. In addition, our spatial analysis model results show that considering various geographic factors help clarify the dynamics of streamflow trends over a large geographical area, supporting a spatial analysis approach over aspatial OLS-estimated regression models for predicting streamflow trends. Results indicate that transitional rain–snow surface water-dominated basins are likely to have reduced summer streamflow under warming scenarios. Consequently, a better understanding of the relationships among summer streamflow, precipitation, snowmelt, elevation, and geology can help water managers predict the response of regional summer streamflow to global warming.

Patrones espaciales de las tendencias de los caudales de marzo y septiembre en el Pacífico Noroccidental.

Los caudales (streamflows) de verano son recursos hídricos vitales para el abastecimiento de agua municipal y domestico así como para el riego agrícola, el hábitat de los salmónidos, la recreación, y para varios servicios de los ecosistemas en el Pacífico Noroccidental (Pacific Nortwest-PNW) de los Estados Unidos. Este estudio identifica tendencias negativas considerables en los caudales absolutos de septiembre en la mayoría de las 68 estaciones de medición situadas en ríos y arroyos no regulares del PNW entre 1958 y 2008. La proporción del caudal de marzo con respecto al caudal anual aumenta en la mayoría de las estaciones situadas a más de 1000 metros de altitud, que tienen un índice de caudal base (base flow index-BFI) de menos de 50, pero se mantiene estable en el resto (la mayoría) de las estaciones. Las tendencias decrecientes de los caudales absolutos de septiembre están fuertemente asociadas con el caudal mínimo para siete días (seven-day low), con las tendencias de temperatura máxima entre enero y marzo, y con el tamaño de la cuenca (19-7,260 km2). Las tendencias crecientes de la proporción del caudal total correspondiente a marzo están asociadas con la elevación, con un equivalente a agua de la nieve de abril (one April snow wáter equivalent -SWE), con la precipitación de marzo, el center timing (TC) de los caudales, y con las tendencias de temperatura mínima entre octubre y diciembre. En comparación con los estimados de modelos de regresión de tipo mínimos cuadrados ordinarios (ordinary least squares-OLS), los modelos de regresión de error espacial (spatial error regression-SER) y de regresión ponderada geográficamente (geographically weighted regression-GWR) eliminan eficazmente la autocorrelación espacial en los residuos. Los resultados del modelo GWR producen mapas con gradientes espaciales donde los valores de los R2 locales son consistentemente más altos en las cascadas del norte. Este resultado pone de manifiesto que diferentes factores hidrológicos del paisaje, tales como la geología y la distribución estacional de la precipitación, también influyen en las tendencias de los caudales en el PNW. Adicionalmente, los resultados del modelo de análisis espacial muestran que la inclusión de diversos factores geográficos ayuda a aclarar la dinámica de las tendencias de los caudales en un área geográfica grande, corroborando la mayor utilidad de modelos con enfoque de espacial sobre modelos. Los resultados indican también que en cuencas transicionales (entre lluvia y nieve) donde predominan las aguas superficiales existe una probabilidad más alta de reducccion de caudal de verano en el contexto de escenarios de calentamiento. En consecuencia, una mejor comprensión de las relaciones entre caudal de verano, la precipitación, el derretimiento de nieve, la elevación y la geología puede ayudar a los gestores del agua a predecir la respuesta de los caudales de verano en un escenario de calentamiento global.

夏季径流是美国太平洋西北部地区(PNW)市政与居民水供应、灌溉、鱼类栖息、娱乐及水相关生态系统服务的重要来源。本研究通过1958–2008年PNW地区68个地理位置上未调节的径流测量站分析揭示出九月绝对径流量与该地区水来源呈显著的负相关趋势。三月径流占年际径流量的比例在大多数海拔超过1000米的地区是增加的,然而大多数地区基本径流指数(BFI)少于50,表明三月绝对径流量在多数地区并没有增加。九月绝对径流量的下滑趋势与年均为期7天的低流量,1月–3月最大温度趋势及流域面积(19–7,260 km2)呈强相关性,而三月绝对径流量微量增加的趋势则与海拔高度,四月一日的雪水当量(SWE),三月降水,径流中心时序(CT)和十月至十二月最小温度趋势相关。与OLS(普通最小二乘法估计)回归模型相比,空间滞后回归(SER)和地理加权回归模型(GWR)能有效剔除空间自相关的残差而更有效。GWR结果显示局部R2值在空间上渐变梯度,并且在北美洲喀斯喀特山脉(Cascade):北部地区高于其他地区。该发现表明不同水文景观因子,如地质、降水的季节分布,也会对PNW的径流趋势产生影响。另外,我们的空间分析模型结果显示,考虑多种地理因素可解析大面积的地理区域中径流量空间分布趋势的动力机制, 为预测径流趋势提供一种优于OLS空间估计回归模型的空间分析方法。结果表明气候变暖背景下,季节性降水、地表水主导的流域极可能减少夏季径流量。因此,更好地理解夏季径流量与降水、融雪水、海拔和地质的关系,可帮助水资源管理者预测区域夏季径流对全球变暖的响应。


Introduction

  1. Top of page
  2. Abstract
  3. Introduction
  4. The study area and data
  5. Spatial statistical analysis
  6. Results
  7. Discussion
  8. Acknowledgements
  9. References

The Pacific Northwest (PNW) of the United States is one of the regions that will be markedly affected by global warming because of the role of mountain snowpack on the region's streamflow (Barnett et al. 2008; Mote and Salathé 2010). Due to its high hydrologic sensitivity to a precipitation phase, the PNW already has been affected by increasing temperature over the past half century. Studies document reduced snowfall (Knowles, Dettinger, and Cayan 2006), decreasing snow water equivalent (SWE) (Mote et al. 2005), earlier snowmelt onset (Stewart, Cayan, and Dettinger 2005), and changes in the timing of streamflow in the water year (Regonda et al. 2005; Hidalgo et al. 2009). These studies show widespread evidence that temperature change can affect snow processes and the seasonal pattern of streamflow. However, questions still remain regarding long-term trends in streamflow due to warming as well as the interaction among changes in hydroclimatic variables and other hydrologic landscape factors (e.g., topography, geology) within a basin. A recent study by Mayer and Naman (2011) provides a good example of research about small-scale hydrologic vulnerability to climate change. They investigated streamflow patterns in the Klamath and Rogue river basins of Oregon and California and found that stream responses to warming vary with both elevation and geology. Groundwater-dominated basins show the greatest absolute reductions in summer streamflow. The usefulness of their findings raises the question about the existence of similar patterns elsewhere in the PNW.

To date, several studies have focused on detecting long-term trends in the PNW streamflow and demonstrated that trends vary substantially according to location and month of the year (Pagano and Garen 2005; Luce and Holden 2009; Clark 2010; Fu, Barber, and Chen 2010; Kim and Jain 2010). However, previous studies employed only a few stations in the PNW, although the region has a dense network of stream-gauging stations located on unregulated streams covering a wide elevation range. This wide spatial and temporal coverage of streamflow data allows for the spatial analysis of the relation between streamflow trends and various landscape factors, including elevation, but few researchers have focused on this feature (Chang and Jung 2010; Kim and Jain 2010; Nayak et al. 2010). Additionally, most previous studies used coarser temporal scales, examining trends in either annual or seasonal streamflow and thus failed to capture the range of possible variation that becomes apparent with finer time-scale analysis (Kim and Jain 2010). Many studies could be enhanced by a thorough consideration of monthly changes in streamflow (McCabe and Clark 2005). This study seeks to improve our understanding of hydrologic response to climate variability across the PNW by identifying long-term trends in monthly streamflow in the unregulated rivers of the PNW and by exploring how these trends and their causes vary across hydrological landscapes. To the authors' knowledge, this is the most detailed study of streamflow trends to date completed for the PNW.

We seek to identify the linkage between monthly streamflow and hydroclimatic variables across heterogeneous hydrologic landscapes. The PNW has an extremely varied hydrology that is associated with different climate, geology, vegetation, terrain, and soil. Primary causes for streamflow changes are expected to differ between hydrologic landscapes, with especially strong contrasts between rain- and snow-dominated landscapes. In rain-dominated low-elevation regions, streamflow change should be immediately influenced by changes in the amount and timing of rainfall. In high-elevation regions, however, snowpack acts as a reservoir that holds water until the energy balance is great enough to melt it. The snowmelt contributes to soil moisture, groundwater recharge, or river flow according to geographic regimes (which reflect such features as geology, topography, elevation, soils, and vegetation). If the melt water infiltrates below the soil into the aquifer system, then regional groundwater dynamics control its fate (Gannett, Manga, and Lite 2003; Tague and Grant 2009; Chang and Jung 2010). In shallow, short flow path groundwater systems, snowmelt-derived flow quickly contributes to river flows in spring and early summer, while in deeper, longer flow path groundwater systems, it may not be released into streams until late summer or later. Consequently, earlier snowmelt can lead to reduced groundwater contributions to streams in late summer (Tague and Grant 2009; Lowry et al. 2010).

The complex interactions among precipitation, temperature, snowpack, streamflow, elevation, and geology have not been fully investigated. Most previous studies assume that the relationships between streamflow trends and various geographic factors are stationary in space and hence employ a single global regression equation. Because of multiple processes of streamflow change in a specific basin, deriving unique local regression model parameters to explain the different relationships between streamflow trends and various factors in different basins in a larger geographic area is reasonable. Such different parameters can be estimated by geographically weighted regression (GWR), developed by Brunsdon, Fotheringham, and Charlton (1998). Here, we apply GWR to explore the possible causes of monthly streamflow trends in heterogeneous landscapes in the PNW.

Specifically, we test the following working hypotheses:

Hypothesis 1. Streamflow trends are spatially variable by month. There is spatial autocorrelation in monthly streamflow trends in the PNW. Hypothesis 2. Streamflow variability and trends are associated with hydroclimatic variables, including precipitation, previous season's temperature, and SWE variables. Late summer streamflow trends are related to a rise in winter and spring temperatures. Hypothesis 3. The response of streamflow trends to temperature warming varies with hydrologic landscape variables, including elevation, geology, and size. Snow-dominated or transient snow–rain basins experience an earlier increase in spring streamflow due to a winter temperature rise. Hypothesis 4. The errors of ordinary least squares (OLS) regression models are not spatially randomly distributed. Spatial error and GWR models can correct for the dependence of errors. Hypothesis 5. The significance of hydroclimatic and hydrologic landscape variables in explaining streamflow trends varies over space.

The study area and data

  1. Top of page
  2. Abstract
  3. Introduction
  4. The study area and data
  5. Spatial statistical analysis
  6. Results
  7. Discussion
  8. Acknowledgements
  9. References

The study area covers basins in the PNW, which includes the Columbia River basin and its subbasins––the Willamette, Deschutes (OR), Snake (ID), Spokane (WA, ID) and other small basins in coastal and interior areas. As precipitation variability in the PNW is strongly influenced by its proximity to the Pacific Ocean and elevation, a strong west–east gradient in precipitation exists. Spatial variability of streamflow generally follows the spatial patterns of precipitation and elevation. High-elevation areas in the Olympic Mountains and the High Cascade Range receive more than 2,500 mm of precipitation annually, much of which falls as snow in the winter, while arid eastern inner regions receive less than 500 mm of precipitation with much smaller seasonal variability. The study area covers 10 different level III ecoregions (U.S. Environmental Protection Agency 2011; see Table 1), encompassing the Coast Range to the Columbia Plateau. Ecoregions are identified by the patterns and composition of biotic and abiotic factors that affect ecosystem quality and integrity (Omernik 1987) and have been used to serve as a spatial framework for the response of ecosystems to environmental stressors and disturbance (Bryce, Omernik, and Larsen 1999).

Table 1. Climatic, Hydrologic, and Geographic Variables Used in This Analysis
VariablesUnitDescriptionType of variablesAnalysis
PrecipitationmmAreal averaged monthly and seasonal precipitationQuantitativeTrend, OLS, SER
SWEmmApril 1 SWEQuantitativeTrend, OLS, SER
Maximum temperature°CAreal averaged monthly and seasonal maximum temperatureQuantitativeTrend, OLS, SER
Minimum temperature°CAreal averaged monthly and seasonal minimum temperatureQuantitativeTrend, OLS, SER
Absolute monthly flowm3/secBasin monthly flowQuantitativeTrend, OLS, SER
Relative monthly flow%Mean ratio of the monthly daily flow to the mean annual daily flowQuantitativeTrend, OLS, SER
BFI%Baseflow index, mean ratio of the lowest annual daily flow to the mean annual daily flowQuantitativeOLS, SER
Seven-day low flowm3/secMinimum value of mean discharge computed over any seven-consecutive days during a yearQuantitativeTrend, OLS, SER
CTdaysCT of streamflow, the days from first day of water year to when half of the water-year flow has passedQuantitativeTrend, OLS, SER
ElevationmAreal averaged elevation of contributing area of each gauging stationQuantitativeOLS, SER
Sizekm2Contributing area of each gauging stationQuantitativeOLS, SER
EcoregionNoneLevel III ecoregion: Blue Mountains, Cascades, Coast Range, Columbia Plateau, Eastern Cascades Slopes and Foothills, Idaho Batholith, North Cascades, Northern Basin and Range, Northern Rockies, Puget Lowland.CategoricalOLS, SER

Daily mean streamflow data for 68 stations throughout the PNW were obtained from the U.S. Geological Survey's U.S. National Water Information System and the Oregon Water Resources Department, and were aggregated into monthly mean streamflows. These stations were selected because they are unregulated, have no notable diversions, and have complete records for water years 1958–2008. The basins cover a wide range of elevations, from 222 m to 2,640 m, representing varying flow processes from rain-dominated to snow-dominated. Fig. 1 portrays the 68 stations and their basin boundaries. To identify the relation between streamflow variability and climatic variables, we used Precipitation Regression on Independent Slopes Model (PRISM) data (Daly, Neilson, and Phillips 1994), which correct spatial orographic effects and have been widely used in climate and hydrologic studies. Assessment of the statistical significance of correlation between streamflow and each climate variable is with a two-tailed Student's t-test using the 5% significance level.

figure

Figure 1. Results of the Mann–Kendall's trend analysis in (a) ratio of March streamflow and (b) September streamflow. The numbers indicate ID of each basin in the Tables 3 and 4.

Download figure to PowerPoint

Snow is an essential driver in the hydrological processes of the PNW (Dettinger and Cayan 1995). To examine the effect of snow cover on streamflow trends, we used the simulated April 1 SWE measurements produced by the variable infiltration capacity (VIC) model (Hamlet et al. 2010) because of a lack of consistent spatial and temporal SWE data over the study basins. VIC is a macroscale process-based deterministic hydrologic simulation model that estimates various water balance components at 1/16th degree resolution at a daily time step, including April 1 SWE. These gridded SWEs are summarized for each study basin and are compared with spatially interpolated snow course data from the National Resources Conservation Service Snowcourse Data Network (http://www.wcc.nrcs.usda.gov/snowcourse/sc-data.html). Observed snow course data from 824 stations are spatially interpolated by cokriging with elevation as the covariate. The linear correlation between simulated and interpolated SWE shows high values (r > 0.50) at high elevations (above 1,000 m) and dense snow course stations, implying the simulated SWE may represent a linear trend based on the observed SWE. Finally, we determined the temporal linear trends in the simulated SWEs and analyzed their spatial relation to streamflow trends.

Other hydrologic variables are derived from annual streamflow statistics (see Table 1). Seven-day low flow is the minimum value of mean discharge computed over any seven consecutive days during a year. Seven-day low flow typically occurs in the lowest flow month. Although September is the end month of the water year in the PNW, the lowest streamflow months occur from August to February in our study basins. Fewer than 40% of the studied basins exhibit lowest streamflows in September (27/68). We thus believe that seven-day flow trends are useful for explaining spatial variations of September streamflow trends. This index has been widely used in ecological and climate change impact studies (e.g., Chang and Jung 2010).

Center timing (CT) of streamflow is the day when half of the water-year flow has passed (Hidalgo et al. 2009). This quantity is an indicator of how winter temperature rise affects snow water content, earlier snowmelt, and associated advances in streamflow CT. This index has been used in climate change impact studies in the western United States (Barnett et al. 2008; Jung and Chang 2011).

Basin mean elevation above each monitoring station was derived from a 10-m digital elevation model. Because runoff-generating processes differ by elevation, we classify basins into three categories following a previous study in the PNW (Perkins and Jones 2008; Chang and Jung 2010): snow-dominated basins (mean elevation over 2,000 m), transient rain–snow basins (mean elevation between 1,000 m and 2,000 m), and rainfall-dominated basins (mean elevation below 1,000 m).

A modified baseflow index (BFI) for each basin was derived from the mean ratio of the lowest annual daily to the mean annual daily streamflow, expressed as a percentage, averaged across all years (after Poff 1996). The quantity derived in this manner is an index useful for comparing basins but not as a measure of total baseflow, as might be derived through hydrograph separation techniques. The modified BFI is used herein as a proxy in the analysis for geology, which has a dominant influence on groundwater hydrology and a large influence on baseflow. The modified BFI is largest in terrains dominated by permeable geology. Permeability is a function of both the lithology (Freeze and Cherry 1979; Fetter 1980) and age (Ingebritsen and Sanford 1998) of geologic materials. Geologic controls on permeability in Oregon are described by McFarland (1983) and Gonthier (1985). The modified BFI used here, however, captures more than simple geology because it is an index of hydrograph “flashiness.” Thus, it most likely is influenced by precipitation, catchment size, and infiltration capacity.

Spatial statistical analysis

  1. Top of page
  2. Abstract
  3. Introduction
  4. The study area and data
  5. Spatial statistical analysis
  6. Results
  7. Discussion
  8. Acknowledgements
  9. References

Trends were analyzed using the nonparametric Mann–Kendall test, which has been used in streamflow trend analysis in previous studies (Hirsch and Slack 1984; Dixon, Lawler, and Shamseldin 2006; Bae, Jung, and Chang 2008; Zhang et al. 2010). Mann–Kendall tests detect significant trends. The null hypothesis (H 0) is that no trend exists in time series data. Therefore, failing to reject H 0 means that insufficient evidence exists to conclude that a trend is present. Equation (1) shows the method for calculating the Mann–Kendall statistics (S). If a time series datum (xk) is greater than the previous datum (xi), S increases by one (sign[xkxi] = 1), while in the opposite case, S decreases by one (sign[xkxi] = −1). If xk equals xi, S is equal to zero (sign[xkxi] = 0). Next, S is normalized (Zc) to remove the effect of S and the sample size (n). Finally, the null hypothesis H 0 states that no significant trend exists if −Z 1−α/2ZcZ 1−α/2, where Zc is a standard normal variable, ±Z 1−α/2 are the standard normal deviates, and α is the significance level. This study uses the significance level of α = 0.10. Although the lower significance level gives a higher chance of rejecting the null hypothesis (providing stronger evidence that suggests more data depart from the null hypothesis to be significant), studies generally use the 0.10 significance level in streamflow trend analysis (e.g., Stewart, Cayan, and Dettinger 2005).

  • display math(1)
  • display math
  • display math

where m denotes the number of tied groups, and ei is the number of points in time in the ith tied group.

We used both absolute changes in monthly streamflow and relative fractional changes in monthly streamflow between 1958 and 2008. This period was chosen because it contains different phases of multidecadal (e.g., Pacific Decadal Oscillation) and multiyear (e.g., El Niño-Southern Oscillation cycle) variability of climates in the PNW. However, the identification of trends relating to warming might be sensitive to the time period used (Dettinger and Cayan 1995; Arnell 1996). The relative fractional change in monthly streamflow is based on the ratio of individual monthly streamflow to annual water-year streamflow. This index has the advantage of accounting for interannual climate variability.

Spatial patterns of streamflow trends are analyzed using the Moran's I global indicator of spatial autocorrelation (Cliff and Ord 1981; Griffith 1987). Because the subbasins are not coterminous, we used the following inverse distance weight within each level III ecoregion:

  • display math(2)

where dij is a measure of the distance between basin i and basin j, and Wij = 0 if the two basins are in two different ecoregions. In other words, even though two basins are adjacent within the study area, if they fall into two different ecoregions, they are not considered to be spatially related (no spatial weight is given to these basins), while two distant basins in the same ecoregion are spatially related.

Similar to a product-moment correlation coefficient, Moran's I is positive if both Xi and Xj lie either above or below the sample mean, while it is negative if one basin value is above the mean and the other basin value is below the mean (O'Sullivan and Unwin 2010). The significance of Moran's I was tested using 499 permutations for a randomization test in the GeoDa package software available at http://geodacenter.asu.edu (Anselin, Syabri, and Kou 2006).

We first selected hydroclimatic and hydrologic landscape variables that have physical meaning in explaining monthly streamflow trends and that are significant at the 5% level using a two-tailed Student's t-test (Table 2). The selected variables differ by month. When multiple consecutive monthly climatic variables (e.g., January maximum temperature and February maximum temperature) are significantly correlated with individual monthly streamflow trends, we use seasonal climatic variables as explanatory variables. The selected variables were entered into stepwise multiple regression procedures to identify the relative importance of each independent variable in explaining variations in monthly streamflow trends. Thus, the final OLS estimated regression equations only include significant variables that do not have multicollinearity problems as indexed by a variance inflation factor less than five (Rogerson 2010).

Table 2. The Significant Pearson Correlation Coefficient Between March and September Streamflow and Climatic and Topographic Variables at the 0.01 Significance Level
StreamflowSizeElevationSWECTSeven-dayP3Tmax_JFMTmax_AMJTmin_OND
March absolute flow 0.414−0.373−0.459 0.5500.458 0.505
March relative flow 0.567−0.327−0.471 0.4680.508 0.502
September absolute flow0.353  0.4570.749 −0.311  
September relative flow   0.5370.512 −0.353−0.369 

We also use spatial error regression (SER) and GWR models to compare the differences in the predictability of streamflow trends between aspatial (OLS-estimated) and spatial regression models. Additionally, we explore whether considering local relations among various geographic factors improve our understanding of streamflow trends in heterogeneous hydrologic landscapes. Compared with OLS-estimated regression models, SER models take into account the spatial autocorrelation among residuals (Ward and Gleditsch 2008). The form of the SER model is

  • display math(3)

where Yi is the dependent variable at location i; Xi is the independent variable at i, βi is the regression coefficient, ɛ is the random error term, λ is the spatial autoregressive coefficient, W ɛ is the spatially lagged error term derived from the weight matrix Wij in equation (2), and ξ is the homoscedastic and independent error term.

The parameters of equation (3) are estimated using maximum likelihood techniques, which involve the eigenvalues of the contiguity matrix (Ward and Gleditsch 2008). Spatial regressions have been applied in water use in Oregon (Franczyk and Chang 2009), a streamflow trend study in Oregon (Jung and Chang 2011), and a water quality study in the Han River basin (Chang 2008). The aforementioned spatial weight matrix is used to develop SER models, and the error terms of each SER model were mapped to check for spatial patterns in these residuals. Spatial autocorrelation and SER regression were performed in the GeoDa software package (Anselin, Syabri, and Kou 2006).

GWR models incorporate local spatial relations into the traditional OLS estimates by allowing the estimation of local parameters. The general form of a GWR model can be described as follows:

  • display math(4)

where i represents each location, a function of the coordinates (ui, vi) for each location is multiplied by the local independent variable xij, and P is the number of independent variables. GWR assumes that observed data near point i have more influence in estimating the values of βji than do the data located farther away from i. Accordingly, an observation is weighted based on its proximity to i. Given that our study basins are not distributed evenly over space, we use an adaptive kernel to define spatial weights. To take into account different ecoregions, basins in the same ecoregion are considered when creating spatial weights, while basins in two different ecoregions are manually separated from each other.

In contrast to OLS-estimated regression and SER models that utilize a constant regression equation, GWR generates multiple regression equations based on individual regional data sets for each basin. Accordingly, a separate parameter and t-value can be estimated for each basin. We mapped these t-values in ArcMap 10.0 (ESRI, Redlands, CA, USA) to inspect visually the spatial distribution of the nature and strength of the relationships among streamflow trends and explanatory variables. The significance of t-values by study basin is calculated in GWR software 3.0. GWR models have been used in air quality (Mennis and Jordan 2005; Harris, Fotheringham, and Juggins 2010), residential water consumption (Wentz and Gober 2007), and water quality studies (Tu 2011; Pratt and Chang 2012).

Results

  1. Top of page
  2. Abstract
  3. Introduction
  4. The study area and data
  5. Spatial statistical analysis
  6. Results
  7. Discussion
  8. Acknowledgements
  9. References

This section reports the results of spatial statistical analysis to test the aforementioned hypotheses. First, we investigate the spatial patterns of monthly streamflow trends with a focus on March absolute flow and September relative flow. Second, we examine the correlation between hydroclimatic variables and streamflow variability and trends. Third, we identify hydrologic landscape factors explaining the variation in streamflow trends. Fourth, we compare OLS-estimated regression with SER and GWR models. Finally, we investigate spatial variation in regression coefficients of the GWR models.

Trends in monthly streamflow

Streamflow trends vary by month and location (Table 3). The fraction of March streamflow to annual streamflow significantly increases in almost one-half (31/68) of the basins. In particular, over two-thirds of the basins over 1,000 m show significant increasing trends. The fraction of April streamflow to annual streamflow also shows a similar trend, although to a lesser degree. In contrast, the fraction of June and September streamflow significantly decreases in 29 and 20 basins, respectively.

Table 3. Results of Trend Analysis of the Ratio (%) of Monthly Streamflow to Annual Flow (Relative Flow) During the Water YearThumbnail image of

The absolute streamflow changes (see Table 4) show similar significant negative trends in the summer months (June–October). In particular, more than two-thirds of the basins' September streamflow significantly decline. March streamflow increases significantly in only 11 stations (16%), although 31 other basins show insignificant increases in March streamflow. Some of the seasonal differences in detecting streamflow trends may be related to the ease of detecting trends in low streamflows due to lower variability (Bowling, Storck, and Lettenmaier 2000). The extreme low-flow index, the seven-day low flow for a water year defined in Table 1, also shows significant negative trends (37 stations; 55% of total stations).

Table 4. Results of the Trend Analysis of Monthly Absolute StreamflowThumbnail image of

A comparison of the changes in monthly fraction of streamflow and absolute streamflow changes reveals an interesting pattern. For some basins that are highly groundwater dominated (BFI > 50), (basin 11, 16, 29), few or no significant trends exist in relative monthly streamflow for all months, while significant declines in absolute monthly streamflow occur for more than half of the 12 months. However, two other groundwater-dominated basins (17 and 34) do not show any significant trends in either absolute or relative monthly streamflow for most months.

An interesting spatial pattern of streamflow trends also exists. Portrayed in Fig. 1, the September absolute streamflow declines are spread over a wide geographical area, regardless of elevation, with weak positive spatial autocorrelation in streamflow trends (Moran's I = 0.213, P = 0.002). March relative streamflow increases only in medium–high elevations and exhibits moderate positive spatial autocorrelation (Moran's I = 0.548, P = 0.002). No coastal basins or valley basins show significant trends in March relative streamflow. These results indicate that trends in monthly streamflow are spatially complex, making identification of comprehensive long-term monthly trends difficult, except in the increasingly dry summer months.

The relation between climate and streamflow variability

To provide insight into the possible causes of decreasing September streamflow, we visually examined trends in winter maximum temperature (January–March), spring maximum temperature (April–June), April 1 SWE, and seven-day low flow using spatially averaged values over the corresponding basin boundaries (Fig. 2). Both winter and spring maximum temperatures increase in most stations (55 and 43 stations, respectively), with significant increases in the northern Cascades in Washington and inner Idaho, respectively. Several stations in southwestern Oregon show a significant decrease in maximum temperatures. Seven-day low flow and April 1 SWE also decline in most stations (60 and 61 stations, respectively), but 37 stations (for seven-day low flow) and 17 stations (for April 1 SWE) show significant declines at the 0.10 significance level. These results indicate that the previous winter and spring months' maximum temperatures have some covariations with decreasing September streamflow trends, but other nonhydroclimatic factors need to be included to increase the statistical explanation.

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Figure 2. Results of Mann-Kendall's trend analysis in (a) winter (January–March) and (b) spring (April–June) maximum temperature, (c) seven-day low flow, and (d) April 1st snow water equivalent.

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Fig. 3 depicts the correlations between August and September streamflow and the corresponding months' precipitation and maximum and minimum temperatures. A significant correlation exists between August streamflow and precipitation for basins lower than 1,500 m. September streamflow also is strongly correlated with September precipitation, mostly for surface water-dominated basins. In contrast, weak correlations exist between September streamflow and precipitation in groundwater-dominated basins. Monthly maximum and minimum temperatures for the same month are not strongly correlated with streamflow for most stations, but 42 stations (62%) show significant negative correlation between maximum September temperature and streamflow.

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Figure 3. The Pearson correlation coefficient of (a) August and (b) September streamflow with monthly precipitation, monthly maximum temperature, and monthly minimum temperature. The dot denotes each station, and the dashed lines indicate the 95% confidence interval. Filled circles indicate a BFI above 20, and opened circles indicate a BFI below 20.

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Fig. 4 depicts the correlation between September streamflow and seasonal precipitation and maximum temperature. September streamflow is highly positively correlated with winter (January, February, March) precipitation in mostly groundwater-dominated basins, while being significantly positively associated with summer (July, August, September) precipitation in surface water-dominated basins. Although not significant in most stations, seasonal maximum temperatures are negatively associated with September streamflow in high-elevation basins (mean elevations greater than 1,000 m). While precipitation amounts between August and September are not strongly correlated for all stations, these months' streamflows are positively correlated with each other, particularly for basins above 1,000 m (Fig. 5). This finding indicates that late summer streamflow changes in the evaluated high-elevation sites are largely composed of baseflow and are therefore unlikely to be solely attributable to precipitation change in corresponding months. Basin geology, as measured by the BFI, also appears to be associated with sustaining late summer streamflow as indicated by a generally higher correlation between August and September streamflows in groundwater-dominated basins (shown in filled circles of Fig. 5).

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Figure 4. The Pearson correlation coefficient of September absolute flow with seasonal precipitations and maximum temperatures. The dot denotes each station, and the dashed lines indicate the 95% confidence interval. Filled circles indicate a BFI above 20, and opened circles indicate a BFI below 20.

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figure

Figure 5. The Pearson correlation coefficient between August streamflow and September streamflow (circle symbols) and between August precipitation and September precipitation (rectangle symbols). The dashed line denotes the 95% confidence interval. Filled circles indicate a BFI above 20, and open circles indicate a BFI below 20.

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As portrayed in Fig. 6, April 1 SWE generally is positively related to September absolute streamflow, particularly in basins over 1,000 m. Except for five basins, all groundwater-dominated basins (BFI > 20) exhibit significant positive correlations between September absolute streamflow and April 1 SWE. In contrast, only 18 stations (38%) show significant positive correlations between September streamflow and April 1 SWE in surface runoff-dominated basins (BFI < 20). However, March relative streamflow does not show any consistent correlations with April 1 SWE, regardless of elevation and geology.

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Figure 6. The Pearson correlation coefficient between (a) SWE and March relative flow and SWE and (b) September absolute flow. Filled circles indicate a BFI above 20, and open circles indicate a BFI below 20.

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The correlation between hydrologic landscape factors and streamflow trends

Fig. 7 portrays the combined correlations of elevation and geology with streamflow trends. As depicted in this figure, transient rain–snow basins, with their mean elevation ranging from 1,000 m to 2,000 m, show significant increases in March relative streamflow, while rainfall-dominated basins do not show any significant increases in March relative streamflow. Basins where BFI is greater than 50 also do not show any significant trends. The correlation between elevation and geology is less pronounced for September absolute streamflow trends, suggesting that other factors need to be considered to explain the spatial variations in September streamflow trends.

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Figure 7. Covariation of elevation and BFI (baseflow index) with (a) March relative flow and (b) September absolute flow trends. The vertical dash line indicates BFI is 20, and the color scheme shows rainfall-dominated (blue), transient (purple), and snow-dominated (white) regions.

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Stepwise OLS-estimated multiple regression models identify four independent variables for explaining March absolute streamflow trends, which are positively associated with March precipitation (P3) trends and mean elevation (Elev), but negatively associated with CT and April 1 SWE (R 2 = 0.62) (Table 5). SER models exhibit the same direction of relationship for each independent variable because spatial autocorrelation impacts only the variance in this specification. Compared to OLS-estimated multiple regression models, inclusion of the autoregressive terms in the spatial regression models explains 5% more variation in March absolute streamflow trends (R 2 = 0.67). The same independent variables originally selected to explain the variations, plus the fall minimum temperature (October–December), explain the variations in March absolute streamflow trends. SER models explain an additional 4% of the variation in streamflow trends (R 2 = 0.73). The relative importance of elevation in explaining the variation in March relative streamflow declines slightly in the SER model, with CT becoming the most significant variable. This finding suggests that the influence of elevation is overstated in OLS estimates.

Table 5. Relationship Between March and September Flow Trends and Climate and Topographic Variables Estimated from Ordinary Least Square Multiple Regression Models and Spatial Error Regression Models (n = 68)
ParameterMultiple regression modelR2
  1. Note: The order of independent variables shows the relative importance of each independent variable. The significance of the t-statistic for each independent variable is used to determine the relative importance of each independent variable. Coefficients were estimated with a maximum likelihood technique. Only significant variables at the 5 % level are included in the final regression models.

  2. P, precipitation; CT, center timing of streamflow; Elev, elevation (in 1000 m); SWE, April 1 snow water equivalent; Tmax, maximum temperature; Tmin, minimum temperature; OND, October, November, December; JFM, January, February, March; λ, autoregressive coefficients; *λ not significant.

March absolute flow  
OLS0.6523 P3 − 0.325 CT + 0.00843 Elev − 0.337 SWE − 0.0080.62
SER0.611 P3 − 0.446 CT + 0.0757 Elev − 0.357 SWE − 0.0078 + 0.4318 λ0.67
March relative flow  
OLS0.0128 Elev − 0.300 SWE + 0.475 P3 − 0.290 CT + 0.150 Tmin_OND − 0.003890.69
SER−0.448 CT + 0.0086 Elev—0.276 SWE + 0.3818 P3 + 0.126 Tmin_OND − 0.0012 + 0.467 λ0.73
September absolute flow  
OLS0.447 Seven-day−0.172 Tmax_JFM + 1.611 Size − 0.0070.62
SER0.441 Seven-day−0.165 Tmax_JFM + 1.784 Size − 0.007 + 0.265 λ*0.65
September relative flow  
OLS0.219 Seven-day + 0.272 CT − 0.301 Tmax_AMJ − 0.0030.44
SER0.246 Seven-day + 0.270 CT − 0.161 Tmax_AMJ − 0.0026 + 0.228 λ*0.46

Absolute September streamflow trends are significantly associated with seven-day low-flow trends, followed by winter maximum temperature, trends in minimum temperature for summer months (July–September) and basin size. September streamflow trends are positively associated with seven-day low-flow trends but are negatively associated with winter maximum temperature trends (Table 4). In other words, basins exhibiting faster increases in winter maximum temperatures also show faster declines in September absolute streamflow. Relative September streamflow trends are significantly positively associated with seven-day low flow and CT. Faster increases in spring maximum temperature are also likely to result in faster declines in the relative proportion of September streamflow.

A comparison of residuals among OLS-estimated regression, SER, and GWR models

Fig. 8 visualizes the degree of spatial autocorrelation in the residuals from three regression models for March relative streamflow and September absolute streamflow. While high residuals are spatially clustered in northeast Oregon and Idaho for OLS-estimated regression models, residuals from the SER and GWR models are spatially randomly distributed with generally lower values of errors. Moran's I-values––global spatial autocorrelation measures––are significantly positive for residuals from OLS-estimated regression models for March relative streamflow (I = 0.12, P = 0.03) and September absolute streamflow (I = 0.17, P = 0.01) at the 5% significance level. In contrast, SER model residuals do not show significant spatial autocorrelation for March relative streamflow (I = 0.00, P = 0.60) and September absolute streamflow (I = −0.04, P = 0.38). Moran's I-values for GWR model residuals are between those for the OLS-estimated regression and SER models (I = 0.03, P = 0.23 for March relative streamflow, and I = 0.12, P = 0.05 for September absolute flow). The sum of absolute errors is lowest for the GWR models and is highest for the OLS-estimated regression models. Because the same weight matrix is used to calculate Moran's I for the residuals and the autoregressive parameters of an SER model, the residuals do not exhibit spatial autocorrelation. GWR models express different spatial relationships among flow trends and explanatory variables from basin to basin.

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Figure 8. The spatial residuals of (a) March relative flow from OLS estimated regression, (b) September absolute flow from OLS estimated regression, (c) March relative flow from SER, (d) September absolute flow from SER, (e) March relative flow from GWR, and (f) September absolute flow from GWR.

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Spatial variations in GWR coefficients

Distinct spatial patterns in local R 2 values are visible in Fig. 9. In general, basins in the northern part of Washington consistently exhibit the highest R 2 values in both March and September streamflow trends. Local R 2 values tend to decline toward the east in March absolute and relative streamflow, and in September, relative streamflow trends. The local R 2 values for March relative and September absolute streamflow trends are higher than 0.8 in most basins.

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Figure 9. The local coefficient of determination (R 2) for GWR for (a) March absolute flow, (b) March relative flow, (c) September absolute flow, and (d) September relative flow.

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As portrayed by Fig. 10, the coefficient values for the April 1 SWE trends, when explaining the variations in March absolute flow trends, are negative and significant in wetter western Washington and Oregon, but the coefficients are positive and insignificant in the drier interior Columbia River basin (eastern Washington and Idaho). The coefficient values for elevation when explaining the variations in March relative flow trends are all positive, but their values are lower and insignificant toward the east, suggesting that the relative correlation with elevation is becoming weaker. The coefficient values of seven-day low flow trends for explaining September absolute flow trends are all positive and significant. The largest coefficient values are found in eastern Oregon and southern Idaho. In contrast, the coefficient values for spring maximum temperature trends, when explaining September relative streamflow, are all negative and are only significant in eastern Washington, northeastern Oregon, and Idaho.

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Figure 10. The spatial variation of the coefficients and significance levels of independent variables (a) SWE in March absolute flow, (b) elevation in March relative flow, (c) seven-day low flow in September absolute flow, and (d) seasonal maximum temperature (April, May, June) in September relative flow.

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Discussion

  1. Top of page
  2. Abstract
  3. Introduction
  4. The study area and data
  5. Spatial statistical analysis
  6. Results
  7. Discussion
  8. Acknowledgements
  9. References

As a comprehensive streamflow trend assessment in the PNW, this study reveals that September streamflow decreased in absolute terms between 1958 and 2008 in a majority of unregulated streams, while the fraction of March streamflow to annual streamflow increased during this time period. Different spatial and temporal patterns of trends exist based on different streamflow indices. The variability in streamflow trends is associated with multiple hydroclimatic and local topographic and geologic factors. First, for basins below 1,000 m, the current month's precipitation becomes more important and is significantly positively related to the corresponding month's streamflow. For basins between 1,000 m and 1,500 m, with mixed effects of rain and snowpack changes, a wide variability in correlation coefficients between September precipitation and streamflow demonstrates that factors other than topography (e.g., geology or vegetation) might contribute to summer streamflow variability. This finding is consistent with other studies in the PNW (Mote 2003; Nolin and Daly 2006; Mayer and Naman 2011). However, we acknowledge that the current research has a sizable multiple testing problem given that we consider a set of statistical inferences simultaneously. As a result, we may have incorrectly rejected some null hypotheses.

As indicated by Moran's I, a distinct spatial pattern exists in September streamflow trends in the PNW. The strong positive spatial autocorrelation in March relative streamflow trends suggests that a spatial gradient of hydroclimatic and topographic factors may be useful for explaining the spatial patterns of March streamflow trends. September absolute streamflow trends show weaker positive spatial autocorrelation than do March relative flow trends, suggesting that other local factors need to be considered for explaining the spatial variability in September streamflow trends.

Notably, streams in the wet western part of the Cascade Range and the Northern Rockies exhibit significantly declining trends, while the small number of sites evaluated in the semiarid eastern part of Oregon, southern Idaho, and southwestern Oregon generally shows no significant trends (Fig. 1). West of the Cascade Range, where basins are predominantly at low elevation and surface water-dominated, the observed declines in September streamflow likely result from decreases in summer precipitation (Fig. 4). Conditions are more variable in the hydrogeologically more complex Cascade Range, whose basins generally show declines (Fig. 1), although not all of the basin trends are significant. The Cascade Range includes both groundwater- and surface water-dominated streams as indicated by the BFI values in Table 3. For example, Cultus Creek (ID 13) and Cultus River (ID 17), two adjacent streams at similar elevations, have BFI values of 0.6 and 72.3, respectively (Table 3). The difference in the groundwater component of streamflow is due to the heterogeneous nature of the geology in the Cascade Range, with some basins dominated by highly permeable fractured lavas, and others dominated by lower permeability glacial or pyroclastic deposits. Consequently, the causes of observed declines are likely variable. Declines in September streamflow in groundwater-dominated basins in the Cascade Range are more likely due to declines in snowpack, as documented by Mote et al. (2005). Declines in surface water-dominated streams are more likely due to declines in summer precipitation. In general, many basins are probably influenced by a combination of these factors.

Additionally, the size of a basin becomes important in explaining September absolute flow trends. The positive sign of the coefficient in multiple regression models implies that in late summer, small streams' flows are likely to be reduced more quickly than large streams' flows. A larger drainage basin can have multiple sources of water delivered to the outlet of a stream in late summer, including delayed groundwater. If the historical rate of warming continues in the future, as most global climate models project, many small streams in the PNW will face water scarcity in summer. Accordingly, ecosystems and communities that rely on water-related services from these streams will become vulnerable.

We also found that the SER and GWR model specifications have advantages over traditional linear model specifications for describing streamflow trends in heterogeneous landscapes such as the PNW. OLS-estimated regression models do not accurately represent the relationship between streamflow trends and explanatory variables. In contrast, SER models capture covariation attributable to some spatially autocorrelated missing explanatory variables, and GWR models capture differences in rainfall–runoff regimes that vary from basin to basin. As portrayed in Fig. 10, the local negative relationship between March absolute flow trends and April 1 SWE trends in humid basins is expected; high March streamflow typically results from earlier snowmelt, and hence, lower April 1 SWE. Because SER and GWR models can capture spatial variation, autocorrelation, and nonstationarity effects more effectively than conventional linear regression models (Fotheringham, Brunsdon, and Charlton 2002), as indicated by several measures reported in this study, SER and GWR models offer potential to help develop accurate streamflow trend models and interpret the effect of explanatory variables. Without considering spatial autocorrelation, OLS-estimated regression models are not likely to overfit model parameters and thus inflate perceived accuracy; the reported R 2 values show an increase for the SER and GWR models. Our analysis, the first application of SER and GWR to streamflow trend analysis to our knowledge, reveals local variation in the streamflow trends and hydrologic landscape factors, and thus, demonstrates the potential of spatial statistical models in streamflow trend analysis.

Accurate prediction of streamflow trends and identification of important geographic covariates allows water resource managers to assess more accurately historical conditions and helps guide future water resource planning and management. Streams experiencing declining September streamflow trends are mostly located near the major population centers of the PNW; if these negative trends continue in the future, municipalities relying on summer water supply from these streams will face potential summer seasonal water shortage problems. Most global climate models predict that the PNW will have hotter and drier summers in the 21st century (Mote and Salathé 2010). If these model projections are correct, the competition among multiple uses, including municipal and domestic water supplies, irrigation, and salmonid populations, will inevitably increase during low streamflow seasons, when most PNW waterways are already overappropriated. Further, reduced streamflow volumes will likely lead to increased water temperatures (Chang and Lawler 2011), with serious implications for salmonid fish populations (Battin et al. 2007). As the hydrologic regime shifts, new storage facilities may be needed in some basins, similar to those suggested for the Upper Colorado River basin (Jain and Eischeid 2008; Rajagopalan et al. 2009). Because the studied basins have free-flowing rivers with no upstream dams or reservoirs, they may be more vulnerable to climate change unless proactive management actions are taken.

Acknowledgements

  1. Top of page
  2. Abstract
  3. Introduction
  4. The study area and data
  5. Spatial statistical analysis
  6. Results
  7. Discussion
  8. Acknowledgements
  9. References

We are grateful to Phil Mote of the Oregon Climate Change Research Institute for his constructive comments on an earlier version of this article. We also appreciate the constructive comments from three anonymous reviewers and editors Daniel Griffith and Elizabeth Wentz, which greatly improved the readability. This research was supported by the U.S. National Science Foundation under grant no. CR-1038925. Additional support for Jung was provided by the Institute for Sustainable Solutions at Portland State University. Views expressed in this material are the authors' and do not necessarily reflect those of the sponsoring agencies.

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  2. Abstract
  3. Introduction
  4. The study area and data
  5. Spatial statistical analysis
  6. Results
  7. Discussion
  8. Acknowledgements
  9. References
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