The importance of non-stationary multiannual periodicities in the NAO index for forecasting 1 water resource extremes

Drought forecasting and early warning systems for water resource extremes are increasingly 15 important tools in water resource management, particularly in Europe where increased 16 population density and climate change are expected to place greater pressures on water 17 supply. In this context, the North Atlantic Oscillation (NAO) is often used to indicate future 18 water resource behaviours (including droughts) over Europe, given its dominant control on 19 winter rainfall totals in the North Atlantic region. Recent hydroclimate research has focused 20 on the role of multiannual periodicities in the NAO in driving low frequency behaviours in 21 some water resources, suggesting that notable improvements to lead-times in forecasting 22 may be possible by incorporating these multiannual relationships. However, the importance 23 of multiannual NAO periodicities for driving water resource behaviour, and the feasibility of 24 this relationship for indicating future droughts, has yet to be assessed in the context of 25 known non-stationarities that are internal to the NAO and its influence on European 26 meteorological processes. Here we quantify the time-frequency relationship between the 27 NAO and a large dataset of water resources records to identify key non-stationarities that 28 have dominated multiannual behaviour of water resource extremes over recent decades. 29 The most dominant of these is a 7.5-year periodicity in water resource extremes since 30 approximately 1970 but which has been diminishing since 2005. Furthermore, we show that 31 resource management practices 16-year periodicity range (centred are two notable peaks in time-averaged wavelet power for the GWL drought the the 7-year periodicity (average wavelet power second 14- 337 year periodicity wavelet modulation of the Chalk (med.mean: 0.16m, med.max: 414 0.34m), similar to GWL in the Limestone (med.mean: 0.35m, med.max: 0.51m) and the 415 Oolite (med.mean: 0.21m, med.max: 0.33m). Lowest overall modulations are found in the 416 Sandstone (med.mean: 0.15m, med.max: 0.25m) and Greensands aquifers (med.mean: 417 0.12m, med.max: 0.17m). Furthermore, prior to this mode of 481 behaviour, an approximate 16-year periodicity predominated the water resource extremes 482 record that did not covary with NAOI. Previous studies have associated a minimum in this 483 16-year cycle in water resources with the wide-scale 1976 drought (Rust et al, 2019) that to the increased non- stationarity of the NAO-precipitation relationship when compared to other regions, which 560 the need for improved low frequency representation in GCMs, and for an understanding of the non-stationary atmospheric behaviours considerably influence wide-scale set out a conceptual model for how multiannual modulations to the may provide a system for improving water resource forecasts and management regimes. This model highlights the need for a systematic understanding of how multiannual periodicities affect water resources over time, including temporal lags and amplitude modulation between the NAO and water resources. We demonstrate that the 658 degree to which the NAO’s 7.5-year periodicity has modulated historical water resources is 659 of a similar order of magnitude to the estimated impacts on water resource variables from 660 climate change projections. These results further show the importance of including the 661 influence of multiannual NAO periodicities on water resources in the understanding of future extremes, as they have the potential to affect the required management regime for certain resources in climate change scenarios. However, we also show that there are notable non- stationarities in NAO periodicities over time and their relationship with water resource response, for which there is limited systematic understanding in existing hydroclimate literature.

may be possible by incorporating these multiannual relationships. However, the importance 23 of multiannual NAO periodicities for driving water resource behaviour, and the feasibility of 24 this relationship for indicating future droughts, has yet to be assessed in the context of 25 known non-stationarities that are internal to the NAO and its influence on European 26 meteorological processes. Here we quantify the time-frequency relationship between the 27 NAO and a large dataset of water resources records to identify key non-stationarities that 28 have dominated multiannual behaviour of water resource extremes over recent decades. 29 The most dominant of these is a 7.5-year periodicity in water resource extremes since 30 approximately 1970 but which has been diminishing since 2005. Furthermore, we show that 31 https://doi.org/10.5194/hess-2021-572 Preprint. Discussion started: 12 November 2021 c Author(s) 2021. CC BY 4.0 License.

Introduction 41
Oscillatory ocean-atmosphere systems (such as El Nino Southern Oscillation (ENSO), North 42 Atlantic Oscillation (NAO) and Pacific Decadal Oscillation (PDO)) are known to modulate 43 hydrometeorological processes over a large domain, often driving multiannual periodicities in 44 hydrological records (Kuss and Gurdak, 2014;Labat, 2010;Trigo et al., 2002). As such, 45 indices of these systems can be useful when explaining decadal-scale variations in water 46 resource behaviour in Europe (Svensson et al, 2015;Kingston et al, 2006), North America 47 (Coleman and Budikova, 2013) and Asia (Gao et al, 2021). In the North Atlantic region, the 48 NAO represents the principal mode of atmospheric variability and is a leading control on 49 European winter rainfall totals (Hurrel, 1995;Hurrel and Deser, 2010). As such, many 50 studies have found strong and significant relationships between the winter NAO Index 51 (NAOI) and hydrological variables across Europe (Wrzesinski and Paluszkiewicz, 2011;52 Brady et al, 2019;Burt and Howden, 2013), leading to the development of seasonal and 53 long-lead forecasting systems of hydrological behaviour (Svensson et al, 2015, Bonaccorso 54 et al, 2015. 55 A growing number of studies have identified stronger relationships between the NAOI and 56 certain water resource variables at multiannual periodicities (Holman et al, 2011;Neves et 57 https://doi.org/10.5194/hess-2021-572 Preprint. Discussion started: 12 November 2021 c Author(s) 2021. CC BY 4.0 License. al, 2019;Uvo et al, 2021), than at an annual scale. This is particularly apparent where longer 58 hydrological response times predominate (Rust et al 2021a). For instance, Neves et al 59 (2019) identified significant relationships between the NAOI and groundwater level in 60 Portuguese aquifers and at approximately 6-and 10-year periodicities, with associations to 61 episodes of recorded groundwater drought. Furthermore, Liesch and Wunsch (2019) found 62 significant coherence between NAOI and groundwater level at approximately 6-to 16-year 63 periodicities across the UK, Germany, Netherlands and Denmark. Rust et al (2019;2021a) 64 identified a similar significant 6-to 9-year cycle across a large dataset of groundwater level 65 (59 boreholes) and streamflow (705 gauges) in the UK, which was associated with the 66 principal periodicity of the NAO (of a similar length (Hurrell et al., 2003;Zhang et al., 2011)). 67 In the instance of groundwater level, this periodicity was found to represent a notable portion 68 of overall behaviour (40% the standard deviation), and minima in the cycle were shown to 69 align with recorded instances of wide-spread groundwater drought (Rust et al, 2019). Given 70 their association with recorded droughts across Europe, these studies highlight the potential 71 benefit of an a priori knowledge of multiannual NAO periodicities in water resources for 72 improving preparedness for water resource extremes in Europe. Here we use extremes to 73 describe water resource deficit (i.e., drought) and periods of anomalously high water 74 resource stores. This is distinct from hydrological extremes, which infers the droughtflood 75

continuum. 76
However, the value of a multiannual relationship between the NAO and European water 77 resources has yet to be assessed in the context of reported non-stationarities in 78 hydroclimate systems. For instance, the NAO is an intrinsic mode of atmospheric variability 79 (Deser et al, 2017), but can also be influenced by multiple other teleconnection systems 80 such as the Madden-Julien Oscillation, Quasi-Biennial Oscillation (Feng et al 2021) or El-81 Nino Southern Oscillation (Zhang et al, 2019). As such it is currently unclear whether 82 periodicities in the NAOI are emergent behaviours or the result of external forcing. This has 83 been compounded by a relatively weak signal-to-noise ratio for NAO periodicities, making 84 https://doi.org/10.5194/hess-2021-572 Preprint. Discussion started: 12 November 2021 c Author(s) 2021. CC BY 4.0 License. confident multiannual signal detection difficult (O'Reilly et al, 2018;Hurrel et al, 1997). While 85 stronger NAO-like multiannual periodicities have been detected in water resource variables, 86 due to the high-band filtering function of hydrological processes (van Loon, 2013), the 87 degree to which these behaviours are sufficiently stable to enable development of predictive 88 utilities is currently unclear. Furthermore, existing research has shown that the sign of the 89 relationship between NAOI and European rainfall is non-stationary at decadal timescales 90 (Rust et al, 2021b); Vicente-Serrano and López-Moreno (2008)). This is expected to add a 91 degree of uncertainty to the detection of lead times between multiannual periodic 92 components in the NAO and water resource response, which is necessary in the 93 development of early warning systems for water resource extremes. While some studies 94 have ascribed lags to this multiannual relationship for European water resources (Neves et 95 al, 2019;Holman et al, 2011), the extent to which this non-stationarity is present at 96 multiannual periodicities has yet to be assessed. 97 Finally, a critical application of early warning systems for water resource extremes is in the 98 design of drought management regimes for existing and projected climate change (Sutanto 99 et al, 2020). While some studies have quantified the degree of modulation that multiannual 100 ocean-atmosphere systems can have on water resources (Kuss and Gurdak, 2014  groundwater boreholes coloured by associated aquifer group, b) jitter plot of groundwater 173 record lengths within each aquifer group, c) location of streamflow gauges coloured by 174 associated regional group, d) jitter plot of streamflow record lengths within each regional group 175 176 177 https://doi.org/10.5194/hess-2021-572 Preprint. Discussion started: 12 November 2021 c Author(s) 2021. CC BY 4.0 License.

Data Pre-processing 179
In this study we use the continuous and cross-wavelet transform to understand behaviours 180 and relationships across different periodicities within the different water resource variable time 181

series. 182
For all datasets, gaps less than two years were infilled to a monthly time step using a cubic 183 spline to produce a complete time series for the wavelet transform. For time series with gaps 184 greater than two years, the shortest time period before or after the data gap was removed. 185 The records were not trimmed to obtain a common period of data coverage. Instead, all data 186 was trimmed to start at a minimum of 1930. This was to allow the analysis of the fewer records 187 that cover a longer time period while still capturing a time periods with adequate record 188 coverage. All of the time series were standardised by dividing by their standard deviation and 189 subtracting their mean. 190

3.2.
Quantifying wide-spread water resource extremes 191 In order to meet objective 1, we produced a time series which describes the behaviour of 192 wide-spread water resource extremes across each resource variable (i.e., groundwater or 193 streamflow). In this study we have assessed water resource extremes using a drought 194 threshold methodology proposed in Peters (2003). While other measures of drought are 195 available (e.g., Standardised Precipitation Index (SPI) and Standardised Groundwater Index 196 (SGI)) (Bloomfield and Marchant, 2013), a threshold approach has been adopted as its can 197 be easily applied to both streamflow and groundwater variables. 198 To calculate a drought series from monthly groundwater level and streamflow series, we first 199 affect the outcomes of the study as the focus is on the frequency structure of water resource 209 extremes, rather than magnitude. 210 For each measurement site, the monthly time series of drought status (whether in drought 211 according to the threshold criteria or not) was converted into a yearly series describing 212 whether that site experienced a drought in the calendar year. Then, for each year, the 213 number of sites that experienced drought were summed and divided by the number of sites 214 with coverage of that year. This produced a time series of the proportion of sites 215 experiencing drought each year, for groundwater level and streamflow variables. This is 216 referred to as the drought coverage time series. 217

Continuous Wavelet Transform (CWT) 219
The Continuous Wavelet Transform (CWT) was performed on the drought coverage time 220 series for groundwater and streamflow to understand the frequency behaviour of wide-221 spread water resource extremes over time. The CWT is often used in geoscience to 222 understand non-stationarities of a variable over time and frequency space (Sang, 2013). We use the package "WaveletComp" produced by Rosch & Schmidbauer (2018) for all 233 wavelet transformations in this paper. 234

Cross-Wavelet Transform (XWT) 235
The bivariate XWT was applied between the NAOI and each of the water resources records 236 (groundwater level (GWL) and streamflow (SF)). This produces a cross-wavelet power which 237 is analogous to the covariance between the two variables over a time and frequency 238 spectrum. This has been selected over the cross-wavelet coherence (analogous to 239 correlation) as this metric requires a high degree of spectral smoothing, making the resultant 240 coherence spectra sensitive to the choice of smoothing approach (Rosch & Schmidbauer 241 (2018))Here we use the covariance spectrum to compare against the drought series 242 frequency spectrum to understand where strong coherences are reflective of dominant 243 behaviours in water resource extremes. 244 https://doi.org/10.5194/hess-2021-572 Preprint. Discussion started: 12 November 2021 c Author(s) 2021. CC BY 4.0 License.
In order to calculate cross-wavelet power (XWP) for the bivariate case, it is first necessary to 245 calculate the continuous wavelet transform (CWT) for each of the variables separately. The 246 XWT between variables x and y is given by: 247 The modulus of the transform can be interpreted as the cross-wavelet power (XWP): 248

Wavelet Significance 250
Lag-1 autocorrelations (AR1) in environmental datasets can produce emergent low frequency 251 behaviours, making the detection of externally-forced behaviours more difficult (Allen and 252 Smith, 1996;Meinke et al., 2005;Velasco et al., 2015). In this study, a significance test was 253 undertaken to test the red-noise null hypothesis that wavelet powers calculated are the result 254 of the recorded variables' AR1 properties. This was based on 1000 synthetic Monte Carlo 255 series with the original AR1 values. In this paper we test significance to the 95% CI. 256 The significance spectra for the XWT for each variable pair (e.g., GWL and NAOI) form the 257 primary results for the XWT method in this paper, since the cross-wavelet power is heavily 258 dependent on the individual series and its frequency composition. The overall relationship 259 between the NAOI and water resources as a whole are investigated by showing the proportion 260 of sites over time and frequency that exhibit a significant relationship with the NAOI (95% CI). 261 This average significance spectrum is produced by summing the significance matrices across 262 each resource (groundwater level or streamflow) and dividing by the number of records used 263 in year each. In the bivariate case, the instantaneous phase difference for the XWP spectrum (between 267 wavelets pairs from the CWT spectrum for each variable) can also be calculated as: 268 This is the difference of the individual phases from both variables at an instantaneous time 270 and frequency (period), converted to an angle between −π, and π. Values close to 0 indicate 271 the two series move in-phase, with absolute values close to π indicating an out-of-phase 272 relationship. Values between 0 and π indicate degrees of phase difference or phase shift. 273 Phase differences between 0 and π can indicate the degree to which variable x is leading 274 variable y, however a phase difference between 0 and -π can either indicate that variable y is 275 leading variable x, or that variable x is leading by more than half the phase rotation (period 276 length). The degree to which a certain variable is leading is analogous to a lag between the 277 two variables. 278 279

Modulation measurement 280
In order to understand the degree of modulation that the NAO teleconnection has on water 281 resources, an absolute and relative modulation value has been calculated for each series. 282 Here, we use modulation to describe the degree to which the NAO (or other process) has 283 increased or decreased a water resource measure from its mean. This has been derived by 284 reconstructing a specific principal periodicity range from the cross-wavelet powers using the 285 following equation: 286 Where dj is the frequency step and dt is the time step. Since the data were standardised by dividing by the standard deviation prior to the wavelet 291 transform, this calculated mean and maximum amplitude are also relative to the sd of the 292 original data. Multiplying the calculated amplitude by the original sd converts this back into a 293 real-valued measurement. This was only done for groundwater, since streamflow is highly 294 dependent on catchment size. In the case of streamflow, amplitudes are reported as relative 295 to the standard deviation of the streamflow record. All calculated modulations were produced 296 using reconstructed wavelets from after 1970 where the majority of records are present in 297 both groundwater and streamflow variables. This was done to mitigate the effect of differing 298 record lengths. 299  13-year periodicity range (greatest power at 11.7 years); region 3: 1960 -1965 in the 2.5-to 326 3.5-year periodicity range (greatest power at 2.8 years); region 4: 1960 -1990 centred at the 327 12-to 17-year periodicity range (greatest power at 15.4 years); and region 5: 1980 to 2020 328 at the 6-to 8-year periodicity range (greatest power at 7 years). There is a sixth significant 329 region starting in 2019 and covering periods between 2 and 5 years, however this is very 330 close to the end of the record and may be subject to edge effects. As such this region has 331 not been taken forward for discussion. 332 There are also two notable non-significant regions of medium strength wavelet power (>=   The cross-wavelet phase difference (ϕ) between water resource variables and the NAOI at 366 the 7.5-year periodicity has been displayed in figure 4 for the GWL records and figure 5 for 367 the streamflow records. The phase difference is a circular measurement where 0 indicates 368 an in-phase relationship (analogous to zero lag) and +/-π indicates an out-of-phase 369 relationship between the selected periodicity within the two variables (analogous to half a 370 periodicity lag (3.75-years)). The purpose of these plots of phase differences are to visualise 371 and understand the difference in phase between the NAO and water resources. Records          Our results show that the dominant mode of multiannual covariance between the NAOI and 463 UK water resources is at the ~7.5-year periodicity. This is apparent in the time-averaged 464 covariance significance plots for groundwater (figure 2b) and streamflow (figure 3b). The 465 same 7.5-year periodicity is also the strongest average mode of periodic behaviour in water 466 resource extremes. Periodicities of similar lengths have previously been detected in 467 European GWL records, such as those in the UK (Rust et al, 2018Holman et al, 2011, 468 Hungary ( Burt and Howden, 2013) and Sweden (Uvo et al, 2021). 471 Our results therefore are consistent with principal periodicities detected in wider European 472 water resources and highlight the NAO's wide-scale control on water resource extremes. 473 Despite the prominence of the average 7.5-year periodicity in water resource variables, the 474 wider time-frequency spectra show that the NAO's multiannual control on water resources is 475 subject to considerable transience and non-stationarity across time and frequency. For 476 instance, the percentage of water resource records with a significant covariance with the 477 NAOI at the 7.5-year periodicity remains below 10% until between 1960 and 1965, with 478 significance becoming abruptly widespread (> 30%) between 1980 and 1985. As such this 479 suggests that the NAO's control on water resources, at the 7.5-year periodicity, has only 480 been prominent over the past four to five decades. Furthermore, prior to this mode of 481 behaviour, an approximate 16-year periodicity predominated the water resource extremes 482 record that did not covary with NAOI. Previous studies have associated a minimum in this Multiple studies have noted a marked change in European hydrological drought trends since 499 the 1970s, often in the context of the ongoing effects of climate change on water resources 500 (Tanguy et al 2021;Rodda and Marsh, 2011;Bloomfield et al., 2019). These impacts vary 501 depending on the water resource and region but can include changing drought frequency 502 (Spinoni et al, 2015;Bloomfield et al., 2019;Chiang et al, 2021), severity (Hanel et al, 2018;503 Bloomfield et al., 2019), and increasing divergence of drought characteristic across Europe 504 (Cammalleri et al, 2020). We show here that a dominant 7.5-year periodicity, driven by the 505 NAO, has occurred coincident to these reported changing trends, and proceeded a 506 secondary periodicity of approximately 16 years. As such our results suggest that some of 507 the change in drought frequency that has been noted to have occurred since the 1970s, may 508 be in-part driven by the NAO's increased periodic control on water resources. Hydroclimate 509 studies often highlight that the interaction between climate change, ocean-atmosphere 510 processes and land-surface processes may be complex, resulting in non-linear hydrological 511 https://doi.org/10.5194/hess-2021-572 Preprint. Discussion started: 12 November 2021 c Author(s) 2021. CC BY 4.0 License. responses to increasing global temperatures (Rial et al 2004, Wu et al, 2018. As such, the 512 abrupt emergence of a 7.5-year periodicity between the NAO and water resource extremes

5.2.
Phase difference between NAO and water resource records at 7.5-year 534 periodicity 535 The quantification of lead times between meteorological processes and water resource 536 response is critical in the development of early warning systems for water resource 537 management. As such, hydroclimate studies have sought to investigate temporal lags 538 between multiannual periodicities in the NAO and water resource variables across Europe 539 (Uvo et al, 2021, Neves et al 2019, Holman et al 2011. However, previous research has 540 highlighted that the relationship strength and sign between the NAO and European rainfall is 541 non-stationary at sub-decadal to decadal timescales (Rust et al 2021, Vicente-Serrano & 542 López-Moreno, 2008. The extent to which this non-stationarity is projected to multiannual 543 periodicities in water resources was previously unknown. Sign change is synonymous with a 544 phase difference shift of approximately π between periodic components of the NAO and 545 water resources, and as such has the potential to disrupt the projection of lead times into 546 future scenarios. Here we assess the phase difference between the NAO and water 547 resources at a country scale to identify the extent to which this non-stationary is present at 548 multiannual periodicities. 549 Most water resources records exhibit an abrupt shift in phase difference of approximately -π 550 around 1990. An earlier shift (of approximately +π) is also apparent between 1970 and 1980, 551 however this is less temporally aligned across the fewer records that cover this period. This 552 suggests that, for the period of approximately 1970 to 1990, the relationship sign between 553 the NAO and water resources was inverted. Furthermore, the timing of this period of 554 inversion generally aligns with reported periods of sign inversion in existing studies between 555 the NAO and UK rainfall (Rust et al 2021, Vicente-Serrano & López-Moreno, 2008. It is 556 interesting to note that this period of inversion is notably shorter for some groundwater level 557 records of the Chalk (e.g., those in South Chalk and Thames and Chiltern Chalk). Rust et al 558 (2021) showed the south and south east of the UK was subject to the increased non-559 stationarity of the NAO-precipitation relationship when compared to other regions, which 560 https://doi.org/10.5194/hess-2021-572 Preprint. Discussion started: 12 November 2021 c Author(s) 2021. CC BY 4.0 License. may explain these relatively short periods of relationship inversion. A similar spatial pattern 561 is shown in the streamflow records, with minimal phase difference shifts in northwest 562 England, Scotland, and Northern Ireland where more stable signs have been found by Rust 563 et al (2021b). 564 Localisation of this non-stationarity between the NAO and water resources at multiannual 565 periodicities suggests it is possible to identify a discrete time period of sufficient stationarity 566 from which to calculate lead-in times for early warning systems (for instance, between 1990 567 and 2020). However, phase differences for this period also show a degree of non-568 stationarity, varying by up to approximately ±¼π. Some of this variance may be due to 569 changing storage dynamics within a catchment over time (Rust et al, 2014;Beverly and 570 Hocking, 2012), but also the introduction of red noise from reconstructing from non-571 significant wavelets. This also explains the increased variance seen in aquifer groups 572 characterised by higher autocorrelation (e.g., Sandstone) (Bloomfield and Marchant, 2013), 573 and the relatively low variance seen in streamflow records which often have lower 574 autocorrelation when compared to groundwater level (Hannaford et al, 2021). While this 575 can be minimised by calculating phase difference from significant wavelets only, we have 576 shown in the previous section that the significance between the NAO and water resources 577 and multiannual periodicities is also subject to notable non-stationarity. 578 Finally, in order to calculate accurate lead-in times between periodicities in the NAO and 579 water resources in future scenarios, a sufficient systematic understanding of the NAO sign 580 non-stationarity is required. However, there is limited research that has investigated the 581 causes for these modes of multiannual non-stationarity. Vicente-Serrano & López-582 Moreno (2008) suggest that an eastward shift of the NAO's southern centre of action may 583 account for a portion of this variability, but highlight that further work is required for this to be 584 a sufficient explanation of a changing correlation between the NAO and European rainfall. 585 As such, existing non-stationarities between the NAO and water resources at multiannual 586 https://doi.org/10.5194/hess-2021-572 Preprint. Discussion started: 12 November 2021 c Author(s) 2021. CC BY 4.0 License.
periodicities remains a considerable barrier to its application in improving preparedness for 587 future water resource extremes. 588

NAO multiannual modulations on water resources in future scenarios 589
Water resource management systems are in place across Europe to improve planning and 590 preparedness for the projected effects of climate change. As such, in order for multiannual 591 NAO modulations of water resources to have sufficient utility for water management systems 592 in future scenarios, they need to exhibit a comparable influence on water resources to the 593 projected effects of climate change. Here, we present historical modulations of summer 594 water resource variables from the principal NAO periodicity alongside expected impacts on 595 water resources from climate change projections in order to discuss their comparative 596 influence. year periodicity. This comparison is provided in  Table 3 from Jackson et al (2015). Median results from the absolute 607 teleconnection modulation on groundwater level from Figure 3 of this paper are also 608 presented for the mean and maximum modulation cases. NAO teleconnection modulations 609 greater than the reported 50 th percentile climate change modulation are shaded in grey. 610 611 612 Historical modulations in groundwater level due to multiannual periodicities in the NAO were 613 greater than projected GWL modulation from a high emissions climate change scenario, in 614 all but two aquifer groups for mean NAO modulation (East Anglia Chalk, Oolite), and all but 615 one for maximum NAO modulation (Oolite  Bloomfield et al. (2003) showed that groundwater levels were 625 expected to rise in the 2020s but fall in the 2050s, and, Jackson et al (2015) showed 626 reductions in annual and average summer levels but increases in average winter levels by 627 the 2050s. For streamflow, Kay et al (2020) give estimated modulations to low flows (Q95) 628 as a result of climate change (2050 horizon). While no Scottish catchments were used in the 629 study, percentage modulations for low flows were found to be mostly between 0 to -20% Europe as a result of climate change, ranging from +20% for northwest Europe to -40% in 633 the Iberian Peninsula. As such, our results for streamflow ( Figure 7) indicate that multiannual 634 NAO modulation of streamflow has been, on average, comparable to the expected change 635 due to climate change scenarios. NAO modulations in streamflow are notably less than 636 those found in groundwater level, as may be expected given the established sensitivity of 637 groundwater processes to long-term changes in meteorological fluxes (Forootan et al., 2018;638 Van Loon, 2015;Folland et al., 2015). 639 Given the scale of multiannual NAO influence on water resource compared to the estimated 640 effects of climate change, the NAO may have the potential to impact the projected trend of 641 water resource variability in certain future scenarios more than was previously understood, 642 and therefore effect the required adaptive management response. However, existing 643 research has shown that that current GCMs do not fully replicate low frequency behaviours 644 in the NAO that have been historical recorded (Eade et al, 2021). Given the importance of 645 multiannual periodicities the NAO in defining water resource behaviour, demonstrated here 646 and in other research (e.g., Uvo et al, 2021;Neves et al, 2019), this raises notable 647 uncertainties in the use of GCMs outputs for projecting European water resource behaviour 648 into future scenarios. Findings reported here suggest that current projections from these 649 GCMs may contain error that is comparable to the current projected effect of climate change 650 on water resources. This therefore highlights the need for improved low frequency 651 representation in GCMs, and for an understanding of the non-stationary atmospheric 652 behaviours are can considerably influence wide-scale water resource behaviour. 653 https://doi.org/10.5194/hess-2021-572 Preprint. Discussion started: 12 November 2021 c Author(s) 2021. CC BY 4.0 License. Rust et al (2018) set out a conceptual model for how multiannual modulations of water 654 resources due to the NAO may provide a system for improving water resource forecasts and 655 management regimes. This model highlights the need for a systematic understanding of how 656 multiannual periodicities affect water resources over time, including temporal lags and 657 amplitude modulation between the NAO and water resources. We demonstrate that the 658 degree to which the NAO's 7.5-year periodicity has modulated historical water resources is 659 of a similar order of magnitude to the estimated impacts on water resource variables from 660 climate change projections. These results further show the importance of including the 661 influence of multiannual NAO periodicities on water resources in the understanding of future 662 extremes, as they have the potential to affect the required management regime for certain 663 resources in climate change scenarios. However, we also show that there are notable non-664 stationarities in NAO periodicities over time and their relationship with water resource 665 response, for which there is limited systematic understanding in existing hydroclimate 666 literature. 667 668

Conclusions 669
This paper assesses the utility of the relationship between the NAO and water resources, at 670 multiannual periodicities, for improving preparedness of water resource extremes in Europe. 671 We review this relationship in the context of non-stationary dynamics within the NAO and its 672 control on UK meteorological variables, as well as its potential impact on water resources in 673 climate change scenarios. We provide new evidence for the time-frequency relationship 674 between the NAO and water resources in western Europe showing that a wide-spread 7.5-675 year periodicity, which predominates the multiannual frequency structure of many European 676 water resources, is the result of a non-stationary control from the NAO between 677 approximately 1970 and 2020. Furthermore, we show that known non-stationarities of the 678 relationship sign between the NAOI and European rainfall at the annual scale are present in 679 water resources at multiannual scales. A current lack of systematic understanding of both 680 https://doi.org/10.5194/hess-2021-572 Preprint. Discussion started: 12 November 2021 c Author(s) 2021. CC BY 4.0 License. these forms of non-stationarity, in existing atmospheric or meteorological literature, is a 681 considerable barrier to the application of this multiannual relationship for improving 682 preparedness for future water resource extremes. However, we also show that the degree of 683 modulation from multiannual NAO periodicities on water resources can be comparable to 684 modulations from a worst-case climate change scenario. As such multiannual periodicities 685 offer a valuable explanatory variable for ongoing water resource behaviour that have the 686 potential to heavily impact the required management regimes for individual resources in 687 climate change scenarios. Therefore, we highlight knowledge gaps in atmospheric research 688 (e.g. the ability of climate models to simulate NAO non-stationarities) that need to be 689 addressed in order for multiannual NAO periodicities to be used in improving early warning 690 systems or improving preparedness for water resource extremes. 691

Data availability. 692
The groundwater level data used in the study are from the WellMaster Database in the 693 National Groundwater Level Archive of the British Geological Survey. The data are available 694 under license from the British Geological Survey at https: 695 //www.bgs.ac.uk/products/hydrogeology/WellMaster.html (last accessed: 24/10/2021). 696 The streamflow data as well as the metadata used in this study are freely available at the 697 NRFA website at http://nrfa.ceh.ac.uk/ (last accessed: 25/10/2021). 698 The data that support the findings of this study are available in CORD at 699 10.17862/cranfield.rd.16866868. This study was a re-analysis of existing data that are 700 publicly available from NCAR at https://climatedataguide.ucar.edu/climate-data.