Seasonal Cross Correlations
 Cross-correlation analysis offers more insight into the relationships between the NCE and the climate variables by examining correlations at specific seasons. Figures 5-8 present the seasonal cross-correlation analysis between the SLD-normalized NCE and PPTr/TEMP anomalies for the USW, USMW, BE, and BW regions, respectively. The USSE and USNE regions show little to no statistically significant correlation results and hence are not shown. Instances in which NCE anomalies lead climate anomalies are due to (1) biased timing in inversion model results, (2) correlations that have no mechanistic relationships, and (3) NCE anomalies that lag climate anomalies by greater than one year, which in this analysis will show up as a lead instead of a lag. For example, a previous study by Bunn et al.  quantified NCE anomalies driven by PPTr anomalies over the BE region and found lags greater than one year.
Figure 5. USW seasonal cross correlation between regional SLD-normalized NCE anomalies and a1) to a5) SLD-normalized PPTr anomalies and b1) to b5) SLD-normalized TEMP anomalies from each of the participating inversion models. Only results that are statistically significant (p < 0.05) are displayed.
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Figure 6. USMW seasonal cross correlation between regional SLD-normalized NCE anomalies and a1) to a5) SLD-normalized PPTr anomalies and b1) to b5) SLD-normalized TEMP anomalies from each of the participating inversion models. Only results that are statistically significant (p < 0.05) are displayed.
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Figure 7. BE seasonal cross correlation between regional SLD-normalized NCE anomalies and a1) to a5) SLD-normalized PPTr anomalies and b1) to b5) SLD-normalized TEMP anomalies from each of the participating inversion models. Only results that are statistically significant (p < 0.05) are displayed.
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Figure 8. BW seasonal cross correlation between regional SLD-normalized NCE anomalies and SLD-normalized TEMP anomalies from each of the participating inversion models. Only results that are statistically significant (p < 0.05) are displayed.
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 In the USW region, all inversions exhibit a negative NCE-PPTr correlation (model mean r = −0.71) suggesting that increases in the precipitation rate (positive PPTr anomalies) are accompanied by intensification of net carbon uptake (negative NCE anomalies), and vice versa (Figure 5a). However, the timing of the correlation between the NCE and PPTr varies among the inversions. Two of the inversions show winter NCE anomalies leading the winter PPTr anomalies by one to two months. The remaining three inversions exhibit spring/summer NCE anomalies with one to two month leads and lags relative to the spring/summer PPTr anomalies. The C13_CCAM_Law also exhibits a broad maximum negative correlation spanning a 9 month lag to a 9 month lead. The roughly coincident spring/summer NCE-PPTr relationship suggests an enhancement of spring/summer rainfall that stimulates increases in net carbon uptake (photosynthetic uptake overcoming respiration release) during the growing season. Similarly, the relationship also implies that episodes of drought are followed by lessened photosynthetic uptake during the growing season.
 The two different seasonal relationships exhibited by subsets of the inversions may reflect the variation in seasonal timing of the vegetation mix in the western US. For example, the US Southwest contains Mediterranean and desert biomes that are less active during summer months versus winter and hence “green up” following winter rainfall anomalies [Hu and Feng, 2004]. Hence, the presence of a winter NCE-PPTr correlation in two of the inversions may be due to atmospheric transport that emphasizes the Southwestern portions of the USW region.
 A significant positive NCE-TEMP relationship is evident for the USW region (Figure 5b). All five inversions show a positive correlation (model mean r = 0.70), with summer/fall NCE anomalies following spring/summer TEMP anomalies. The positive correlation between NCE and temperature anomalies could suggest either increasing carbon release (respiration or fire) or weakened photosynthesis accompanying higher temperatures, and vice versa. Research utilizing NDVI measurements proposed a decline in carbon uptake in mid- to high latitudes due to warmer and drier summers [Angert et al., 2005]. However, other studies that have examined both photosynthesis and respiration response to temperature in the US West have concluded that respiration is more sensitive [Allen et al., 2005; Anderson-Teixeira et al., 2010] and that higher temperatures increase ecosystem carbon loss from the decomposition of dead plant material [Kirschbaum, 1995].
 Both the NCE-TEMP and NCE-PPTr relationships in the USW are consistent with the impacts of drought, which are associated with elevated temperature and reduced precipitation [McDowell et al., 2008]. There has been a well-documented increase in the duration, intensity, and frequency of drought in the USW which has been referred to as “global change-type droughts” [Breshears et al., 2005]. Higher temperatures and reduced water availability increase the energy load and water stress on vegetation, which result in greater vegetation mortality. Furthermore, this can also lead to greater amounts of dry woody material that is susceptible to bark-beetle infestations and wildfires, which have also been increasing in frequency and duration in the USW since the mid-1980s [Westerling et al., 2006; van Mantgem et al., 2009]. This drought-vegetation relationship is consistent with the NCE correlations found here for the USW. For example, negative PPTr anomalies during the extreme 1999–2004 drought period are correlated (model mean: r = −0.68) with positive NCE anomalies in the USW region at lags of ~ 6 months. Climate change projections for the USW suggest that vegetation will experience more water stress because of the effects of higher temperature on evaporation rates [Seager, 2007]. Our findings suggest that warmer and drier conditions will result in greater carbon emissions, and that the combined effect has the potential to reduce carbon stocks and net ecosystem productivity in the USW region.
 In the USMW region, a negative NCE-PPTr correlation (four model mean r = 0.60) is found for four models, with summer/fall NCE anomalies following spring/summer precipitation anomalies (Figure 6a). The negative NCE-PPTr correlation indicates that enhanced spring/summer rainfall results in greater net carbon uptake during the growing season, and vice versa. This is supported by Lu et al. , which found that precipitation increases cause greater NPP over the USMW. For the NCE-TEMP relationship, a positive correlation (four model mean r = 0.6) is found for four models (Figure 6b). Three models show summer/fall NCE anomalies following summer TEMP anomalies, while one (C13_CCAM_Law) indicates a lead relationship. The positive NCE-TEMP correlation implies that increased temperature anomalies lead to weakened photosynthetic uptake during the growing season, and vice versa. However, given the discrepancy in the timing of the NCE-TEMP relationship in the USMW, this result is ambiguous.
 In the BE region, a negative correlation is found between the NCE and PPTr anomalies for four inversions (four model mean r = −0.60) (Figure 7a). However, the timing of the relationship varies. Three inversions show summer NCE anomalies following fall PPTr anomalies in the previous year. One inversion shows spring NCE anomalies following summer PPTr anomalies in the previous year. The negative NCE-PPTr correlation suggests that PPTr increases intensify carbon uptake during the growing season and vice versa, and that this response lags the PPTr anomalies by almost one year. This relationship suggests that increased precipitation (snowpack) in fall influences conditions in the following summer through ground ice and soil freeze-thaw processes [Schaefer et al., 2007; Matsumura and Yamazaki, 2012]. The resulting increase in the growing season water table depth and water availability inhibits nighttime respiration leading to increased net carbon uptake [Dunn et al., 2007]
 The NCE anomalies are positively correlated (model mean r = 0.65) to TEMP anomalies for all inversions in the BE region, with summer/fall NCE anomalies following close behind summer TEMP anomalies (Figure 7b). The positive association indicates that increases in temperature weaken net carbon uptake and vice versa. This finding is consistent with the study of Piao et al. , in which they suggest that autumn warming would cause a greater response to respiration than photosynthesis, thus leading to a decline in net carbon uptake.
 In the BW region, however, our analysis does not show any significant NCE-PPTr relationship. Other studies have found that increased water content suppressed NCE in western boreal black spruce forests in the late summer and fall [Krishnan et al., 2009]. This discrepancy may be ascribed to the diversity of plant types in this region as well as their difference in responding to climate variability [Goetz et al., 2005]. By contrast, NCE anomalies for the BW region are negatively correlated to TEMP (four model mean r = −0.68) in four of the five inversions, with winter/spring NCE anomalies correlated to summer/fall TEMP anomalies (Figure 8). This negative NCE-TEMP correlation implies that enhanced winter/spring carbon uptake responds to a warmer summer/fall time period in the previous year. These findings for the BW region are consistent with previous studies using both satellite remote sensing and field observations. For example, studies based on multidecadal NDVI data proposed a “greening” photosynthetic trend in high latitudes, which is tied to spring/early summer shrub expansion in tundra ecosystems [e.g., Bunn et al., 2007]. A number of recent studies indicate that the shrub expansion appears mainly in Alaska and western Canada, which is linked to greater early growing season carbon uptake driven by winter and spring warming [Welp et al., 2007]. Some studies have found this northward shrub expansion correlated to summer warming in the previous year, consistent with the BW negative NCE-TEMP relationship found here [Blok et al., 2011].
 Why does an NCE-TEMP dipole relationship appear in the two boreal regions in the context of widespread warming in the northern latitudes, as suggested by the results presented here? This could be driven by vegetation in the two regions responding similarly to temperature variations but that the two regions exhibit an opposing temperature variation. Alternatively, the two regions may have the same temperature variation, but the vegetation response to temperature in the two regions exhibit an opposing response. Finally, a combination of the two may be occurring.
 An examination of the SLD-normalized TEMP anomalies in the two regions does indeed show dipole behavior (Figure S3.3, in supporting information) supporting the notion that the relationship has to do with the regional climate variations. For example, Wang et al.  found that opposing temperature variations in the two regions drove the Spring/Summer between NPP and temperature using 15 years of NDVI. These opposing temperature anomalies may be driven themselves by snowpack anomalies and the impact they have on surface temperatures.
 However, ecosystem structure is also likely an important factor in the dipole NCE-temperature relationship. The BW region is predominantly tundra while the BE region is predominantly forest [Zhang et al., 2008]. Hence, a vegetation-specific response to temperature anomalies may play a role [Goetz et al., 2005; Zhang et al., 2008]. The precise mixture of vegetation response versus climate variation in boreal NA remains a topic of future study.