The importance of year-to-year variation of meteorological and runoff forcings for water quality of a temperate , dimictic lake

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Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | 1 Introduction Natural stochasticity sometimes presents challenges in maintaining the quality of the environment. Such is the case with reducing nutrient loading in the hope for making the quality of downstream lake better. Natural variation in weather for example may confound costly abatement efforts by counteracting the abatement of nutrient loading. In particular, nutri-5 ent loading is determined both by hydrology (partially determined by meteorological forcing on land) and by the management effort (agriculture and urban related nutrient loading). Furthermore, weather may also be directly consequential in lake processes such as algal growth. Under this kind of challenge, it is paramount to evaluate to what extent the confounding variable can actually make significant differences in lake water quality . The 10 present study illustrates how a variance-based modelling method could disentangle two major factors affecting a lake, with a test case study of eutrophication recovery of a Norwegian lake.
The scientific community has learnt that nutrient enrichment of lakes may lead to high phytoplankton mass development, low water transparency, and fish mortality due to oxygen 15 depletion (Smith et al., 1999). Mainly two factors affect the nutrient loading to lakes: (1) the soil and land use in the lake catchment, and (2) the hydrology of the watershed. Phosphorus is generally regarded as the limiting nutrient for phytoplankton production in freshwater lakes (Schindler, 1977). Much effort has therefore been given to reduce phosphorus input to aquatic ecosystems, which has demonstrably led to reduced phytoplankton production and 20 increased water transparency in many lakes in Europe and North America (Jeppesen et al., 2005). On the other hand, many lakes have showed delayed or negligible improvements in water quality despite reduced nutrients loading (Jeppesen et al., 2007a).
Year-to-year weather variations have also been recognised to affect physical, chemical and biological processes in lakes (Bailey-Watts and Kirika, 1999;Blenckner et al., 2007;25 Jeppesen et al., 200925 Jeppesen et al., , 2007bWhitehead et al., 2009). Increase in air temperature has been shown to increase the water temperature (George et al., 2007) and the stability of thermal stratification (Straile et al., 2003a), change the phytoplankton community towards Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | dominance of species adapted to warmer water (Weyhenmeyer et al., 2002), and possibly lead to earlier and higher phytoplankton production (Huber et al., 2008;Weyhenmeyer et al., 2002). Changes in thermal conditions and mixing regime can in turn influence the light, oxygen and nutrient dynamics in lakes, and thereby impact the phytoplankton primary production and community structure (Tirok and Gaedke, 2007;Wilhelm and Adrian, 2008).  cipitation is also deemed as an important factor in determining water transparency, runoff intensity, and suspended matter discharge (Arheimer et al., 2005;Nõges et al., 2007;Ulén et al., 2007).
Norway has, generally, a low fraction of arable land (3 %) and low population density (12 persons km −2 ), so eutrophication is mainly recognizable in intensive agricultural districts 10 at low altitudes. Lake Årungen is situated in a developed agricultural area south-east in Norway, and is one of the most nutrient rich lakes in the country. Geological studies suggest that the natural phosphorus concentration of lakes in this area is 7-8 mg m −3 (Borch et al., 2007). Eutrophication became a problem in the lake during the 1960s, with phosphorus concentration exceeding 400 mg m −3 in the 1980s (Løvstad and Krogstad, 1993). Algal 15 blooms, low water transparency, malodorous water, reduced fish stocks, and occasional mass mortality of fish were observed in the lake in this period (Ensby et al., 1984). Despite investments in sewage treatment and extensive changes in agricultural practices since the 1970s to reduce nutrient leaching and erosion from the catchment, algal growth is still high. Predicting eutrophication responses to nutrient loading is a complex task due to the 20 stochastic dynamics of lake's response to weather, the confounding factor. Here we used one of the lake models (MyLake) (Saloranta and Andersen, 2007) based on system of processes that have been identified as a primary tool for improving our understanding of recovery and progression of eutrophication (Mooij et al., 2010). More precisely, we made combinations of forcing data (meteorological and nutrient loading inputs) for the model, with 25 1. some forcing data being the actual records and 2. others being the average day-to-day record for the period of 16 years, repeated 16 times.
Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | This approach criss-cross the day-to-day and year-to-year variability in a systematic way, and simulation outputs based on dissimilar combinations of these "actual" and "repeated avarage year" can be analysed once again from the day-to-day and year-to-year variability. In principle, the actual data are more variable than the repeated average year. If a particular forcing variable is significant in affecting the lake water quality, switching from the actual to 5 repeated average year reduces the year-to-year variation in lake water quality variables. Combinations of these two types of forcing data are described in Sect. 2.5. This approach of comparison by opting in the average year for a selected variable is used in a slightly different context by Jöhnk et al. (2008), with a difference being that the "average year" was taken from one candidate year in Jöhnk et al., while the "average year" in the current study 10 was indeed day-of-year-specific year-to-year average. More importantly, the current study demonstrates the use of year-to-year variance for each day of year, which is a powerful visual and quantitative tool in detecting the critical season for a variable.
The separation of two temporarily varied factors affecting the same environmental receptor is not only useful in lake water quality modeling. For example, agricultural yield and 15 forestry are affected by weather, soil conditions, diseases, and tilling and fertilisation amount and timing. Other examples may be climate change impacts on physical landscape, such as glacial extent or surface water ice cover, which are affected by stochastic meteorological conditions and warming forcing which are mostly anthropogenic but also of natural origin (e.g., volcanic activities), as well as regional multi-year fluctuation such as the North Atlantic 20 Oscillation or El Nino.
The main aim of the current study is to evaluate the relative importance of year-to-year variation of two major factors, namely meteorological forcing and nutrient loading, contributing to lake's physical, chemical and biological conditions. We also visually inspect how their respective significance varies over the season. To this aim, (1) the MyLake model (Salo-25 ranta and Andersen, 2007) was first calibrated against the lake data, (2) then various meteorological and nutrient loading scenarios combining variation of these two major factors were applied, and finally (3) the predicted lake responses were compared among different Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | scenarios, in particular, the variance among years, rather than the absolute value of the predictions.

Study site
Lake Årungen is a dimictic lake with maximum and average depths of 13 and 8 m, respec-5 tively. The lake is located in south-east Norway (59 • 41 18 N, 10 • 44 38 E; Fig. 1), 25 km south of Oslo, and has a surface area of 1.2 km 2 . The catchment area covers 51 km 2 , where 53 % is agricultural land, 34 % forestry, 10 % densely populated and 3 % open water surfaces. The lake is highly exposed to agricultural runoff that causes high nutrient and particle loading. Runoff is mainly through 6 streams of 1.5 to 5 km length. The outlet connects 10 the lake to the marine environment as Lake Årungen enters the Oslofjord through a 3-km long stream.

Model
MyLake is a one-dimensional lake model, adapted from MINLAKE (Riley and Stefan, 1988), which simulates daily changes in physical and chemical dynamics over the depth gradient 15 (Saloranta and Andersen, 2007). The model simulates ice and snow dynamics in a mechanistic manner and it has been applied to winter-freezing lakes in Norway and Finland (Kankaala et al., 2006;Lydersen et al., 2003;Saloranta et al., 2009;Saloranta, 2006;Couture et al., 2014). It was therefore considered as a suitable model for Lake Årungen. 20 MyLake requires input of meteorological forcing, runoff volume and temperature, and fluxes of suspended inorganic particles and total phosphorus (TP) to model phosphorus and phytoplankton dynamics in the lake (Table 1). Meteorological data for daily air temperature, Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | global radiation, cloud cover, precipitation, relative humidity and wind speed were obtained from the nearby meteorological station located at the Norwegian University of Life Sciences (59 • 39 37 N, 10 • 46 54 E). Direct measurements of daily runoff volume, runoff water temperature, and fluxes of suspended inorganic particles and total phosphorus to the study lake Årungen was not available. However these values were estimated using the Skuterud 5 monitoring station (Fig. 1) with a hydrovolumetric weir at which these runoff variables were monitored (1994)(1995)(1996)(1997)(1998)(1999)(2000)(2001)(2002)(2003)(2004)(2005)(2006)(2007)(2008)(2009)(2010), providing accurate flux at this subcatchment. In order to account for runoff contributions of different types of landuse in the other subcatchments, such as agriculture and urban build up, we used previously determined scaling factor that both correct for flow and nutrient factors (Askilsrud, 2010). The monitoring station is located at an in-10 let stream to Østensjøvann (59 • 41 18 N, 10 • 49 45 E), a small lake of 0.4 km 2 which drains into the Lake Årungen (Deelstra et al., 2007). A separate MyLake model was set up for Lake Østensjøvann to account for the buffering effects of this lake in the largest sub-catchment of Lake Årungen. The simulated water properties of Lake Østensjøvann were combined with runoff from the other sub-catchments as an estimate of the total runoff to Lake Årungen. 15 Six variables including whole-lake average TP pool, mean surface chlorophyll concentration, light attenuation coefficient, thermocline depth, epilimnion temperature, and ice thickness were calculated from unprocessed model outputs (Table 1) in order to ease interpretation of the statistical analyses for scenario experiment described below. 20 Water temperature, TP, soluble reactive phosphorus (SRP), and chlorophyll a concentration from the deepest location in the lake were used to calibrate the model (Table 1). Vertical water temperature profile was continuously logged every hour at eight depths between 0.7 and 12.6 m by Hobo pendant temperature loggers (model 64K-UA-002-64; Onset Computer Corporation, Bourne, MA, USA) in the period from November 2008 to August 2010. 25 Water samples for chemical and biological analyses were collected with a modified Ruttner water sampler at seven depths twice a month or monthly (n = 49) from January 2008 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | to September 2010. TP, SRP and chlorophyll a were determined spectrophotometrically (UV-VIS Spectrophotometer UV-1201, Shimadzu, Kyoto, Japan).

Model calibration
We deployed the Markov chain Monte Carlo (MCMC) method (Andrieu et al., 2003;Saloranta et al., 2009) during the calibration procedure. The calibration consisted of two stages. The first MCMC calibration stage involved three physical parameters ( Table 2) that only af- 5 fect heat dynamics, in particular thermocline depth. This first calibration was run against daily temperature measurements, using 2000 MCMC steps with the first 1000 for burn-in. The second MCMC calibration stage involving eight parameters ( Table 2) that affect phosphorus and chlorophyll dynamics, but not temperature, was run against measurements of TP, SRP, and chlorophyll a in 30 000 MCMC steps with the first 10 000 for burn-in. For exam-10 ple, algal growth in the MyLake model is a function of nutrient concentration, light availability and water temperature, and amplitude of these factors were controlled by parameters. In the present study, runoff was given as external input to the model, and water temperature and underwater light conditions were determined in the first stage of MCMC. Therefore, for the example of algal growth, the second stage of MCMC only changed the amplitude 15 of algal growth in response to these external factors. For these MCMC applications, convergence was monitored visually. Linear interpolation was used to match model outputs on a 0.5 m vertical grid to the actual measurement depths. Although it was not used directly during the MCMC calibration, model goodness of fit was informally assessed by root mean square error (RMSE). The medians of the posterior parameter distributions generated from 20 both stages of the MCMC calibrations were used for the scenarios experiments described in the following.

The variance-based method for disentangling confounding factors
The model was run under four scenarios for nutrient loading and weather in order to quantify the respective impacts of weather variation and loading conditions on phosphorus and 25 phytoplankton dynamics (Table 3). Runoff volume (in the runoff group) is predominantly influenced by precipitation (in the meteorology group), but runoff volume was kept together with runoff concentrations because the most important influence the runoff has is the to-Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | tal amount of nutrients, which we obtain by multiplying concentration by volume. These scenarios were based on input combination of observed data (original data, 1994-2010) and synthetic data, where the synthetic data were created by taking the year-to-year mean (n = 16) of each of the days of year. Synthetic data repeats the calculated mean year with 365 days sixteen times. The 29 February is removed in year-to-year mean calculation, and 5 28 February was repeated to account for the 29 in leap years.
This approach combines the actual forcing data for some variables together with average year data for the other forcing data variables. Comparing such a synthetic scenario against the scenario using full actual forcing data elucidates importance of year-to-year variation of the second set of variables. For example, scenario C (repeated average-year runoff) will 10 necessarily have lower year-to-year variation (n = 16) in output variables compared with scenario A (full original data) (Table 3); the difference in the scenario input (i.e. runoff input) accounts for the reduction in the year-to-year varition in the output variables. By examining which output variables are most reduced in year-to-year variation among all output variables, we obtain crucial information on the importance of runoff forcing data in the output. 15 Thus we achieved the the goal of the present study, namely disentangling the relative importance of year-to-year variation of two major factors (meteorological and loading inputs). The idea of mixing actual and average-year forcing data were derived from the study conducted by Jöhnk et al. (2008), in which the authors assessed the relative importance of various meteorological variables (air temperature, cloudiness, wind speed) in affecting various lake 20 responses such as water temperature and algal cell counts of 3 phytoplankton groups. The present study compares standard deviation of the 16 years of simulation outputs for each day of year for 6 output variables among several sceniarios.
Combining the repeated average input together with actual stochastic input (such as in the scenarios B and C, Table 3) causes unrealistic input for two reasons. One reason is 25 the inconsistency among variables on the daily basis. For example, because runoff is controlled by precipitation, the scenario C for instance (original weather + averaged runoff) on a daily basis may suffer from a potentially undesirable situation such as high precipitation with no cloud on a certain day. This is unrealistic, but from the lake ecosystem perspective, Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | the runoff's role is mostly as the source of nutrient, and weather as the source of energy, and the fact that the lake water is accumulation of old water from runoff introduced many days ago, the influence of this inconsistency in combination is minimal. The second reason is that the intra-variability or within-year variability that naturally stochastic variables such as meteorological inputs should have is lost in the present study's design. This can 5 cause problems such as not providing extreme wind events due to averaging despite such wind events may be crucial for the on-set of ice formation, or determination of thermocline. Hydrodynamic models are therefore usually driven by stochastically generated time series (Semenov et al., 1998;Schlabing et al., 2014). Alternatively, most average looking year could have been chosen as in Jöhnk et al. (2008). However, the current study requires the 10 average to be done on multiple criteria or variables, making a choice of one year as the average year for a certain variable will not necessarily be the average year on all the variables at the same time. Due to the purpose of reducing the year-to-year variation and not to be particularly bound by a selected single year or randomly generated year, repeated average year was used despite these potential problems. In the present study, year-to-year variation 15 in outputs of these four scenarios will be discussed but not the actual values on the daily basis, and the results are interpreted with care that scenario A is the most variable on a year-to-year basis, that either B or C is the next, and finally that D is the least, although this care does not completely safeguard the results from unrealistic intra-year varitions or incosistencies. 20

Post-simulation methods
All the data analysis and statistical analyses were done using R (version 3.1.2, R Core Team (2014)). A two-way analysis of variance (ANOVA) was run on the 16 years of water year based simulation statistics (water year mean, see Table 1), among scenarios A, B, C and D (two weather factors by two loading factors, see Table 3). All annual averages are computed 25 over the period from 1 October to 30 September, commonly used in Europe to refer on a hydrological year, or a water year (Otnes and Raestad, 1978). Since treatment contrasts are nested within water years we factored out the between-year variances to gain a greater Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | power in the statistical tests. Principal component analysis (PCA) was used to explore the relationships between meteorological and land-related forcing and their relevance for the simulated lake response. Four water years with extreme PCA scores were selected for studying contrasting lake responses in closer details.

Calibration
The simulated water temperature and thermal dynamics of the lake were in agreement with the lake observed data. Observed water temperature measurements were well predicted by simulation and the RMSE was less than 2 • C at all lake depths (Fig. 2). After the water temperature calibration, parameters controlling TP, SRP, and chlorophyll a were cal-10 ibrated against observed data for the period from January 2008 to September 2010. The epilimnion TP, SRP, and chlorophyll a concentrations were well predicted by the model, although their prediction was less successful than the prediction of the water temperature. The TP and SRP were better predicted by the model in pelagic surface water than in deep water whereas the chlorophyll a showed the opposite pattern. In general, the model simu-Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper |

Variability in forcing data
Inter-annual variation was expressed as the standard deviation in inputs and outputs between the years. All weather inputs varied between years (Fig. 3), with air temperature and global radiation having the strongest seasonal pattern in inter-annual variation (i.e. greater 16 year variation as compared to year-to-year variation on a day-of-year basis). The 5 inter-annual variation in air temperature was strongest in the winter period, whereas global radiation varied most during the summer months. The variation in cloud cover, precipitation and relative humidity was generally similar across seasons. The year-to-year variation for precipitation was particularly high in December and in the period from July to September, the latter reflecting extreme precipitation events. Wind speed varied most in winters. 10 Runoff input data on water flow and concentrations of TP and suspended matter all varied seasonally and between years. The variation in runoff volume was greatest in the period from October to May. No clear seasonal pattern in the degree of variability could be found for suspended matter and TP fluxes, although the variation of TP influx seemed to peak in February-March. 15

Variability in simulation outputs: disentangled significance of confounding factors
Differences in year-to-year variation among the scenarios (Fig. 4) and the annual statistics (Table 4) illustrate the seasonal influence of the external forcing on the thermal regime and the phosphorus and phytoplankton dynamics in the lake. There is a large amount of 20 N in Årungen, as N is applied in surplus at the agricultural fields. Even though there is some reduction in N during summer, N is excluded as the limiting nutrient (Romarheim, 2012). The lake responded differently between years; all simulated outputs, except ice thickness, showed large variation in the beginning and at the end of the phytoplankton growing season (Fig. 4). All simulated output variables were influenced by external forcing as they 25 varied inter-annually for all model scenarios (see variance decomposition in Table 4). Ice thickness was significantly affected by weather (P < 0.001) as both air temperature and Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | winter precipitation highly contributed to its variation between years (Table 4; Fig. 4). The variation in thermocline depth in May and October was well revealed by the model, and seemed to be equally dependent on weather and loading. The epilimnion temperature during the whole growing season was largely controlled by weather. The TP content in the lake was most variable in the period from November to January, and in April and July. Loading 5 could mostly explain the inter-annual TP variation in the lake, whereas precipitation contributed to TP variation only in the spring, and air temperature only during the winter period. Loading was the overall most important factor in controlling the light attenuation coefficient (P < 0.001) and surface chlorophyll concentration (P < 0.001). Weather seemed to be important in controlling chlorophyll and light attenuation in early spring whereas loading was 10 the most important factor controlling the both variables from June to September. The yearto-year variation in these two variables from June to September under the scenario C was higher than scenario A, despite that scenario C is less variable year-to-year than scenario A in loading. This might be because scenario C may distribute the autumn runoff events that is still significant after spreading over the years, and this might have caused the light-related 15 variables to be unstable on a day-to-day scale. The years 1996The years , 2000The years , 2006The years and 2007 were the four most extreme years determined on the basis of the PCA analysis (Fig. 5). The year 1996 was characterized by relatively low average annual air temperature, a thin cloud cover and low precipitation, which resulted in low epilimnion water temperature, short lasting thermocline, low runoff volume, and TP 20 in the lake. The year 2007 represents an opposite to 1996 regarding weather characteristics, resulting in a model simulation with relatively high average annual air temperature and precipitation. Increase in wind speed, decrease in air temperature, and decrease in precipitation coincided with increase in ice thickness and glocal radiation, such as in 2003-2006, 2009, and 2010. These weather conditions resulted in lower suspended inorganic particles 25 and TP in runoff which coincided with lower surface chlorophyll concentration and light attenuation. The year 2006 was identified to be extreme during this period, with a cold winter followed by a warm summer. In contrast, the year 2000 was characterized as a year with less global radiation, lower summer air temperature, and higher wind speed, but with higher Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | winter temperature and precipitation. Such weather conditions pronounced higher TP and suspended particle in runoff compared with an average year, resulting in a high surface chlorophyll concentration and lower water transparency.
The methodological choice of using a repeating average year (see Section 2.5) may have reduced the impact of extreme weather events but probably caused little difference in the 5 overall interpretation and conclusion. But the result that the daily year-to-year variation for either scenario B or C was closely following scenario A, depending on the modelled variable (TP content, surface chlorophyll, light attenuation coefficient for scenario B, and ice thickness, thermocline depth, and epilimnion temperature for scenario C) provides confidence that the conclusions will not change due to the methodological limitation.

Year-to-year variability in lake responses
Year-to-year weather variations, as well as the influence of catchment land-use and hydrology, hinder our understanding of how individual stressors may affect the lake response (Blenckner, 2005). Our model experiment, which involved the input of weather and loading 15 data for 16 years, was able to outline the respective importance of year-to-year variation in external forcing on physical, chemical and biological response in Lake Årungen. The combination of high forcing variability and high lake response sensitivity made the inter-annual variation most dramatically expressed in spring and autumn.
Air temperature, precipitation, and wind speed are the principal factors influencing fresh- 20 water ecosystems in a changing climate (Nickus et al., 2010). The lake thermal regime was to a large extent affected by weather conditions, particularly by air temperature. Variable winter air temperatures were an important factor influencing the heating and mixing processes during spring. A dynamic physical environment at the beginning of the growing season has considerable influence on the phytoplankton community structure and its dynamics 25 (Weyhenmeyer et al., 2002). For example, increased surface water temperatures in the En-Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | glish Lake District (George et al., 2007) and incomplete water mixing in Lake Constance (Straile et al., 2003a) have earlier been associated with mild winters. High inter-annual variation in winter air temperatures in Lake Årungen was reflected in the simulated ice thickness and phenology of ice formation, with ice forming in December-January and disappearing in March-April. Likewise in other lake studies, thinner and shorter ice cover has been re-5 lated to mild winters (Nickus et al., 2010). In this study, the timing of thermocline formation varied among years by more than one month, from mid-April to mid-May. The large yearto-year variation in thermocline depth and duration could lead to changes in temperature, light, and nutrient condition in the lake, which further shape the phytoplankton community and determine its total biomass Zohary et al., 2010). For instance, 10 early disappearance of diatoms and high development of cyanobacteria in European lakes has been related to winter warming and increased water temperature (Weyhenmeyer et al., 2002). Furthermore, increase in water stability favours the buoyant phytoplankton species such as bloom forming cyanobacteria (Reynolds et al., 1983;Winder and Hunter, 2008).
Year-to-year variation in phosphorus content in the lake was highly influenced by nutri-15 ent loading. This indicates that the external nutrient supply remains an important source of phosphorus in the lake. Although the changes in nutrient loading are primarily linked to anthropogenic activities in the catchment, in particular to practices in agriculture, the shortterm variations in weather and runoff can also influence the nutrient supply from external sources. Lake Årungen is surrounded by agricultural land, and is especially sensitive to vari- 20 able weather conditions that promote nutrient loading from the catchment. More precisely, air temperature and rainfall frequency and intensity affect the runoff and the soil erosion pattern, particularly during the winter period. Increase in winter temperatures occuring together with frequent freezing and melting events increases the risk of erosion, which again will increase the nutrient loading to the lake ( Nõges et al., 2007). Although not statistically demonstrated in the present study, the indirect impacts of weather conditions on discharge may still be important in regulating the nutrient dynamics. Variable winter weather conditions, and the timing of ice out were most important cause of year-to-year variable phosphorus content in the period from November to January Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | and in April in Lake Årungen. Enhanced phosphorus concentrations in streams during winter and high phosphorus loading in early spring both contribute to the total lake phosphorus concentration during the following summer in two Norwegian lakes with agricultural catchments (Bechmann et al., 2005). In addition, the variation in summer TP content could also be the result of between-year variation in rainfall, especially due to extreme precipitation 5 events as observed for particular days in July. High inter-annual variation in TP content can consequently result in variable phytoplankton biomass between years.
Phytoplankton biomass and light were significantly affected by loading, although atmospheric forcing also contributed to their inter-annual variation in the lake. The effect of loading was pronounced during the whole algal growing season, whereas weather had the 10 strongest effect in early spring and from mid-August to the end of the growing season. Thermal stratification is highly dependent on weather and may further influence water mixing as well as light and nutrient regimes, which are important in controlling the phytoplankton dynamics Zohary et al., 2010). Similar patterns of year-to-year variation in water temperature, chlorophyll concentration, and light attenuation indicate a close 15 relationship between these variables. Higher air temperature promoted higher water temperature and higher stability of the thermal stratification which enhanced phytoplankton production of bloom forming cyanobacteria (Reynolds et al., 1983;Weyhenmeyer et al., 2002). Runoff and soil erosion, caused by intense precipitation and frequent melting of snow and ice during mild winters, affect eutrophication and water turbidity (Bechmann et al., 2005;20 Jeppesen et al., 2009). Thus light may limit phytoplankton growth more than nutrients in highly turbid lakes such as Lake Årungen (Dokulil, 1994). Reduced light availability may be crucial for the competitive success of cyanobacteria which are functionally adapted to low light conditions (Litchman, 1998). Particularly high dominance of cyanobacteria has been observed in the Lake Årungen after mild winters followed by low light conditions in spring 25 (Romarheim et al.,unpublished). Therefore, additional measures to control soil erosion may need to be implemented in water management, not only to reduce the supply of nutrients, but also to avoid low water transparency which may favour development of potentially toxic cyanobacteria.
Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | 4.2 Implications for lake management According to our PCA analysis, most of the 1990s were categorized by winters with higher temperatures and more rainfall. The mild winters were related to a positive North Atlantic Oscillation (NAO) phase which has been shown to strongly influence physicochemical and biological responses in western European lakes (George et al., 2007;Straile et al., 2003b;5 Weyhenmeyer et al., 2002). The effect of climate condition on water ecosystems, however, should be considered individually as the lake response is also determined by the lake's geographical position, landscape topography, and the lake's morphometry and mixing regime (Nickus et al., 2010). Our model experiment indicated that greater inflow of suspended matter and phosphorus to the lake Årungen is expected after mild winters with high precip-10 itation. Consequently, higher chlorophyll concentrations and greater light attenuation were predicted after mild and wet winters such in the year of 2000. Mild winters may thus counteract measures aimed to reduce external nutrient supply and to control phytoplankton production in cold temperate lakes, appearing to have contributed to little improvement. On the contrary, cold winters were related to thicker ice layer, less inflow of suspended matter 15 and phosphorus, and low chlorophyll and light attenuation. This was consistent with the observed increase in water transparency and reduction of phytoplankton biomass, particularly of cyanobacteria, in Lake Årungen after the cold winter in 2010 (Romarheim et al., unpublished). Special attention must therefore be given to management practices, which should minimize the use of fertilizers and reduce the risk of nutrient runoff and soil erosion, 20 especially in areas that drains directly into the lake. Higher annual air temperature coincided with warmer epilimnion, shallower thermocline and extended summer stratification such as for the year of 2007. In addition, high annual precipitation and runoff volume, particularly in summer, coincided with warmer years.
Globally, all years in the period from 1995 to 2006, with an exception of 1996, were among 25 the warmest since 1850 (Trenberth et al., 2007). Likewise, the year 1996 was characterised with low average annual air temperature in our model experiment. Lower annual air temperature and low rainfall in 1996 led to low epilimnion temperature, and a deep and short lasting Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | thermocline. According to future climate predictions for Scandinavia, warmer winters and increased winter precipitation are expected in south-eastern Norway (Hanssen-Bauer et al., 2005). If so, we should also expect more intensive soil erosion, higher phosphorus loading, lower water transparency, and greater phytoplankton biomasses, primarily of cyanobacteira in the lakes. Global climate changes and inter-annual variations in the local weather both 5 directly, and indirectly through an impact on the catchment, influence the physicochemical and biological processes in lakes. The limnological and biogeochemical knowledge of this lake identified by decomposing year-to-year variation of the two factors, carries potential in connecting future management. Runoff is partially controlled by precipitation which in turn is predicted to change, and so are air temperature and global radiation. Therefore, the effect 10 of climate should be considered in future decision-making concerning water management.  Freshwater Biol., 52, 1647-1666, doi:10.1111/j.1365-2427.01773.x, 2007 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Hanssen-Bauer, I., Achberger, C., Benestad, R. E., Chen, D., and Forland, E. J.: Statistical downscaling of climate scenarios over Scandinavia, Clim. Res., 29, 255-268, doi:10.3354/cr029255, 2005. Huber, V., Adrian, R., and Gerten, D.: Phytoplankton response to climate warming modified by trophic state, Limnol. Oceanogr., 53, 1-13, doi:10.4319/lo.2008.53.1.0001, 2008 Jeppesen  Environ. Qual., 38, 1930-1941 Jöhnk, K. D., Huisman, J., Sharples, J., Sommeijer, B., Visser, P. M., and Stroom, J. M.: Summer heatwaves promote blooms of harmful cyanobacteria, Global Change Biol., 14, 495-512, doi:10.1111/j.1365-2486.01510.x, 2008 Methanotrophic activity in relation to methane efflux and total heterotrophic bacterial production in a stratified, humic, boreal 30 lake, Limnol. Oceanogr., 51, 1195-1204, doi:10.4319/lo.2006.51.2.1195, 2006 Population and community responses of phytoplankton to fluctuating light, Oecologia, 117, 247-257, doi:10.1007Oecologia, 117, 247-257, doi:10. /s004420050655, 1998 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Table 2. Parameters involved in calibration based on two-stage Markov chain Monte Carlo (MCMC) application (first stage for three parameters using 2000 MCMC steps with 1000 steps for burn-in and second stage for eight parameters using 30 000 MCMC steps with 10 000 for burn-in). MyLake equation numbers refer to the original model description (Saloranta and Andersen, 2007). Median values were chosen among the posterior parameter distribution.

Parameter Value Equation Unit
Prior distribution

Physical parameters
Open-water vertical diffusion coefficient 7.56 × 10 −3 Eq. (10) Minimum possible stability frequency 9.31 × 10 −5 Eq. (10) s −2 1.14 × 10 −4 × 10 x where x ∼ N(0, 1)   Figure 1. Map of catchment draining into (1) Lake Årungen, with the (2) weather station at Ås, (3) Lake Østensjøvannet and (4) the Skuterud monitoring station. Runoff data from the Skuterud subcatchment (indicated by dark shading) are scaled up according to land area and usage of the rest of the catchment to estimate the total loading to Lake Årungen.    Table 3 for scenario configurations. Black coding for PC loading indicates the weather input, brown the runoff input, and blue the lake simulation.