RECONSTRUCTIONS OF HYDROLOGIC VARIABLES IN THE NORTH PLATTE RIVER BASIN OF HYDROLOGIC VARIABLES IN THE NORTH PLATTE RIVER BASIN.”

: Reconstructions of hydrologic variables are commonly created using tree-ring chronologies (TRCs) to generate information about historic climate and potential future variability. This study used TRCs to reconstruct annual streamflow, April 1st Snow Water Equivalent (SWE), and soil moisture in the North Platte River Basin (NPRB). Stepwise linear regression was performed to determine which of the 55 moisture sensitive TRCs were the best predictors of hydrologic variation. The regressions explained 63% of the variability in streamflow, 55% of the variability in SWE, and 66% of the variability in soil moisture. This study then maximized the overlapping period of records which resulted in a decrease in the percent of variability explained but indicated that the regression models were stable for long reconstruction periods. This study successfully reconstructed all three hydrologic variables for NPRB to 1438 or earlier. Temporal wet and dry periods for streamflow and SWE were closely aligned while soil moisture did not follow similar temporal patterns. This was likely due to a natural “lag” between soil moisture and streamflow / SWE given soil moisture tends to retain antecedent signals. The availability of reconstructed hydrologic data in NPRB allows for a better understanding of the long-term hydrologic variability in the region .


Introduction
Hydrologic variables are essential factors when evaluating the overall climatic condition of a watershed. Streamflow, April 1st snow water equivalent (SWE), and soil moisture are three of the predominant hydrologic variables in the North Platte River Basin (NPRB). The availability and sustainable use of surface water are major issues in the western United States (U.S.). Deficiencies in long-term streamflow data hamper sustainable water resource management which relies heavily on detailed information associated with natural hydroclimatic variability (Watson et al. 2009). In 1993, Loaiciga et al. reviewed the methodology and applications of streamflow reconstructions using tree rings and found that ring widths in climate sensitive trees can be reliable indicators to describe past hydroclimatic conditions. The estimated magnitude and duration of hydrologic droughts from streamflow reconstructions using tree-ring records are important water management resources and provide a strong link between dendrochronology and hydrology (Meko et al. 2012).
Longer and more robust streamflow reconstructions help to provide additional information on present and future extreme dry and wet events (Meko et al. 2007). Successful streamflow reconstructions have been conducted across the western U.S. using tree ring chronologies (TRCs) and have been used for assessing hydrologic drought scenarios (Cook et al. 1999; Meko et al. 2001). Several studies have reconstructed streamflow in the regions surrounding the NPRB Meko et al. 2007; Watson et al. 2009; Barnett et al. 2010) and Soukup et al. (2009) performed long lead-time forecasting in the NPRB for unimpaired streamflow stations.
When evaluating streamflow reconstructions, it is also beneficial to look at SWE and soil moisture values. Runoff from snowpack, which is influenced by soil moisture levels, occurs during the spring and early summer. April 1st SWE is commonly used to represent the maximum seasonal snowpack (Woodhouse 2003;Kuhn 2005;Timilsena and Piechota 2008). Early summer snowmelt from mountains in northern Colorado and southern Wyoming is the primary source of streamflow in the North Platte River (Shinker et al. 2010). Variability in North Platte SWE drives variability in streamflow and water availability for the Colorado River Basin.
Soil moisture is a key factor in the conversion process of precipitation into runoff and groundwater storage and, in that manner, is influential in the development of wet or dry periods (Tang and Piechota 2009). In temperate climates, the growth of trees closely depends on the heat and moisture availability of soil, making TRCs a useful predictor for reconstructions of past environments (Yin et al. 2008). Evans and Trevisan (1995) developed a water-balance "bucket" model which illustrated how variations in soil moisture transform the structure, species composition, and abundance of vegetative coverage. Fan and van den Dool (2004) produced a soil moisture dataset from 1948 to present based on the one-layer "bucket" water balance model. This dataset provides monthly soil moisture, evaporation, and runoff data for a 0.5⁰ × 0.5⁰ global grid.
In this paper, streamflow, SWE, and soil moisture are reconstructed for the NPRB using TRCs. These hydrologic variables are examined in conjunction with each other to identify relationships between the three. The reconstruction of these variables augments the existing limited records of hydrologic data and may provide significant benefits to water managers in the NPRB for analyzing the historical wet and dry periods.

Study Area
The NPRB is located in northern Colorado and southern Wyoming (Fig. 1). The headwaters of the North Platte River originate in the high basin of North Park (north-central Colorado) (Acharya et al. 2011). The North Platte River is a tributary of the Platte River and is considered a major drainage avenue for eastern Wyoming and western Nebraska (Shinker et al. 2010

Streamflow Data
The United States Geological Survey (USGS) collects surface water data across the U.S. Data are collected by automatic recorders and manual field measurements (USGS 2013

Tree-Ring Chronologies
For the majority of the western U.S., Meko et al. (1995) determined that tree ring widths are a proxy for gage records because the same prime climatic factors, namely precipitation and evapotranspiration, control both the growth of moisture-limited trees and processes related to streamflow. Fifty-five TRCs were used for the reconstruction of the three hydrologic variables examined in this study. These TRCs were obtained from the International Tree-Ring Data Bank website (http://www.ncdc.noaa.gov/paleo/treering.html), and are the same TRCs that were used in the previous hydrologic reconstructions in South Platte River Basin and western Wyoming Residual TRCs were selected to reduce the possibility of low-order autocorrelation caused by changes in growth factors (Fritts 1976). Of the 55 TRCs, 14 were created from ponderosa pine (Pinus ponderosa), 22 from pinyon pine (Pinus edulis), 15 from Douglas-fir (Pseudotsugamenziesii), two from lodgepole pine (Pinus contorta), one from limber pine (Pinus flexilis), and one from Engelmann spruce (Piceaengelmannii). All six of these species are considered to be moisture sensitive (Fritts1976; Woodhouse and Lukas 2006).

Correlation and Stability Check
Statistical analysis is a method of determining the quality and suitability of TRCs for reconstruction of climatic variables ). Streamflow, SWE, and soil moisture were individually correlated with each of the 55 TRCs using Pearson's correlation method (Timilsena and Piechota 2008). For temporal stability checks between TRCs and each of the hydrologic variables, correlation coefficients between the two were calculated for a 20-year moving window. TRCs that were positively and significantly correlated at a confidence of 90% or greater for all windows were retained. This process was repeated independently for streamflow, SWE, and soil moisture. [63]

Regressions
Stepwise linear regression (SLR) is a common approach for the reconstruction of hydrologic variables using TRCs (Woodhouse 2003 The variance infiltration factor (VIF) is used to measure multicollinearity in a model. For models with more than one predictor variable, the largest VIF is analyzed. A VIF equal to 1 indicates there is no multicollinearity in the model. However, if the VIF is between 5 and ten, then the model is not considered statistically valid because the regression coefficients are poorly estimated.
The R 2 value indicates the percentage of variation explained with the regression equation and ranges from 0 to 1. The higher the R 2 value, the better the model represents the data. An R 2 value of 0.40 or higher is considered successful for hydrologic reconstructions (Woodhouse 2003; Timilsena and Piechota 2008).
Predicted R 2 values indicate how well a model predicts responses for additional observations and is used to prevent an overfitting tendency of the model. It explains the relationship between the predictor and response variable, although it fails to provide valid prediction in new observations. A predicted R 2 value significantly less than the R 2 value indicates that the regression model will not predict future responses based on new observations as well as the model fits existing data. Predicted R 2 values are calculated based on a drop one cross validation technique where one observation is removed from the datasets and the remaining observations are used to predict the missing value. The value for predicted R 2 ranges from 0 to 1.

Model Refinement
The overlapping periods of record between the TRCs and the hydrologic variables was limited by the fact that many of the trees used to develop the chronologies were cored in the late 1970s. For the preliminary reconstructions, this study used all 55 TRCs. The overlapping period of record started when the data for the hydrologic variable began and ended in 1978. For the subsequent reconstructions, this study selected the models from the preliminary analysis that yielded statistically strong results and refined them by maximizing the overlapping period between the TRCs and the hydrologic variables. Since the preliminary analysis had already determined which TRCs were retained for each hydrologic variable, the subsequent analyses were based only on these retained TRCs. This allowed the overlapping period of record to be limited by the shortest end year of the selected TRC(s) rather than the shortest end year of all 55 TRCs. For example, in the preliminary reconstruction of streamflow performed in this study, the overlapping period of record was 1916-1978 (streamflow record began in 1916, the shortest of the 55 TRCs ended in 1978), and two TRCs (PUM and TRG) were retained. In the subsequent reconstruction of streamflow, two TRCs were considered (PUM and TRG) and the overlapping period of record was 1916-2002 (streamflow record began in 1916, the shortest of the two TRCs ended in 2002).

Streamflow Reconstruction
Fifty-five TRCs were correlated with streamflow data and tested for stability, resulting in four retained chronologies. These four TRCs were entered as predictors into the SLR model and two TRCs were selected. The reconstruction model using these two TRCs explains 63% of the variance in streamflow (

SWE Reconstruction
Reconstructions were developed for the 11 SNOTEL stations with sufficient periods of record in the NPRB. The reconstructions explained 29 to 55% of variance for the various stations and used between 1 and 5 TRCs. The Dry Lake station (DLK) had the highest explained variance (55%) and is shown in Fig. 1

Soil Moisture Reconstruction
Regression models were developed for each of the five soil moisture grid cells contained within the NPRB. The number of retained predictors varied between 1 and 3. The regression results for the five cells explained 36,37,40,54, and 66% of variance in the soil moisture. The cell with the highest explained variance (66%) is centered at 253.25°W longitude and 41.25°N latitude and is shown in Fig. 1 and Table 1. The D-W statistic indicates no autocorrelation is present. The model is statistically valid having a VIF below 5. The model is statistically similar to the successful reconstruction of soil moisture by Anderson et al. (2012a) in the UCRB.

Refined Model Comparison
Once the preliminary regressions had been completed, the process was repeated with an aim to maximize the overlapping period. Only retained TRCs from the previous regression models of hydrologic variables were used in the SLR model. Although both the R 2 value and the predicted R 2 value declined from the preliminary regression models (Table 2), the refined regression models provide a longer overlapping period with the observed (streamflow, SWE, soil moisture) variables. The NPRB streamflow reconstruction, which begins in 1404, provides data for a longer period than the extended streamflow reconstruction of the main-stem Green River gage near Greendale, Utah produced by Barnett

Retained Tree-Ring Chronologies
The varying moisture sensitivity of different tree species is a significant controlling factor behind the variability of the reconstructed hydrologic variables (Anderson et al. 2012a). Previous research efforts attributed the difficulty of reconstructing hydrologic variables in the adjacent Green River Basin (Timilsena and Piechota 2008) and Wind River Basin (Watson et al. 2009) to the lack of moisture sensitive TRCs in the region. Within and adjacent to the NPRB, 55 moisture sensitive TRCs were available, which contributed to the success of the current reconstructions and compared favorably to the reconstructions of Woodhouse and Lukas (2006) in South Platte River Basin. In all of the reconstructions performed in this study, only six unique TRCs were retained (PUM, TRG, MCP, GMR, ENC, and RUS). Three of these TRCs (PUM, TRG, and MCP) were developed from pinyon pine cores, two (GMR, ENC) were developed from Douglas-fir cores, and one (RUS) was developed from ponderosa pine cores. The streamflow reconstruction relied solely on TRCs developed from pinyon pines, the SWE reconstruction used TRCs developed from pinyon pines and Douglas-firs, and the soil moisture reconstruction used TRCs developed from pinyon pines, Douglas-firs, and ponderosa pines.
The geographic location of the moisture sensitive tree is an important indicator for capturing soil moisture in a given area (Anderson et al. 2012a). Ponderosa pines are the most widely distributed pine species in North America (Mast et al. 1998) and are generally found in the Rocky Mountains. Pinyon pines are found in cold, semiarid climate and are abundant in the lower mountainous region of western Colorado and extend to southern Wyoming (Evans, R. A. 1988). Douglas-firs are found in low and middle elevation forest areas of Colorado over a wide range of aspects, slopes, landforms, and soils (De Velice et al. 1986). Developing additional chronologies from pinyon pines across the NPRB could improve the skill of the streamflow, SWE, and soil moisture regressions as this species was useful in reconstructing all three types of hydrologic variables.

Comparison with Observed Hydrology
Observed streamflow was compared with reconstructed streamflow over the calibration period.
Of the three driest years on record (1934,1954,1977), the observed and reconstructed values match fairly well for two of the years (1934,1954), while for the third year (1977) the reconstruction portrays 1977 as being drier than the observed value. In the wettest years on record (1918,1957,1984,1997), flows are consistently underestimated (Fig. 2a). This systematic underestimation of extreme high flow years is common in tree-ring studies (Gray et al. 2011 (Fig.3). The two datasets match well in the late-1600s, mid-1700s, and mid-1800s. Given the similar geographical location of these two studies, the comparable data trends give merit to these generated reconstructions.
Although 48% of the variance in SWE is explained by the model, this statistic does not provide an evaluation of how well the reconstruction represents extreme SWE values (high and low). Dry extremes are better replicated than wet extremes in moisture sensitive trees, as trees are limited in growth by dry conditions but not usually by wet conditions (Woodhouse 2003). Through assessment of the SWE calibration period, this study found that the reconstructed SWE closely modeled many of the driest years on record (1962, 1976, and 1994), although the reconstruction shows 1968 as being drier than the observed SWE (Fig. 2b). Reconstructed SWE for extremely wet years (1952, 1957, and 1978) is consistently low.
Observed and reconstructed soil moisture data were standardized (mean of zero, standard deviation of one) across the calibration period (Fig. 2c). Extreme high and low moisture levels are well represented by the reconstruction.

Climatic Variability of Hydrologic Variables in the NPRB
Reconstructions of hydrologic variables for the NPRB provide critical insight into the patterns of natural variability of streamflow, SWE, and soil moisture. These hydrologic variables are important when assessing the sensitivity of the North Platte River to current or future climate change. The streamflow and SWE reconstructions created in this study cover five centuries. Similar to Anderson et al. (2012b), this study found a strong relationship between streamflow and SWE. Both reconstructions indicate that the years 1460, 1510, 1590, 1670, and 1850 were extremely dry and the years 1490, 1620 and 1680 were extremely wet (Fig.4). Changes in soil moisture can amplify climate extremes such as flood or drought (Tang and Piechota 2009). In four of the five years that streamflow and SWE reconstructions suggest were extremely dry (1460, 1590, 1670, and 1850), reconstructed soil moisture is very low. This indicates that soil moisture reconstructions can provide an insight into hydrologic droughts (Figure 4d). Figure 4: Graphical representation of reconstructed hydrologic variables (a) reconstructed streamflow using a 10-yr filter, (b) reconstructed April 1st SWE using a 10-yr filter, (c) reconstructed soil moisture (standardized) using a 10-yr filter, (d) standardized streamflow, standardized April 1st SWE, and standardized soil moisture using a 25-yr filter

Conclusions and Recommendations
Reconstructions of hydrologic variables are important factors for assessing the overall climatic scenario of a watershed and deducing the hydroclimatic variability in the western U.S. This study suggests that TRCs can be used as proxy records to represent hydrologic variables for a long-term perspective. The strong relationship between the streamflow and SWE reconstructions, and the fact that SWE volume directly impacts streamflow volume, suggests potential drought could be anticipated when the magnitude of spring snowpack is known. Future research should focus on