dynamic links between climate and environmental change · ter precipitation, over more than a time...

Dynamic Links between Climate and Environmental Change 11

Dynamic Links between Climate and Environmental Change

Ronny Berndtsson1, Jonas Olsson2, Bellie Sivakumar3 and Kenji Jinno4

1 Department of Water Resources Engineering & Center for Middle Eastern Studies, Lund University, Lund, Sweden

2 Research and Development, Swedish Meteorological and Hydrological Institute, Norrköping, Sweden

3 Department of Land, Air and Water Resources, University of California, Davis, USA4 Department of Earth Resources Engineering, Kyushu University, Fukuoka, Japan

Abstract: In this paper we investigate dynamical properties of temperature, precipitation, and runoff to the Baltic Sea. We find that these variables appear to display nonlinear relationships that can be approximated by chaotic trajec-tories in time-space. The major climatic driver for this behavior appears to be the solar input. We argue that dynamic univariate and multivariate prediction meth-ods would work well to predict the future environmental state of the Baltic Sea since the major nutrient input follows the natural inflow of runoff to the sea.

IntroductionAn important aspect of climate change is environmental effects on large water bodies. Such a large water body is the Baltic Sea. The Baltic Sea is the largest brackish water body on Earth and consequently of great interna-tional concern. The Baltic drainage basin spans 14 countries and 85 million people, a majority of them living in big cities like St. Petersburg, Copen-hagen, Helsinki, Tallinn, Riga, Vilnius, Warsaw, and Stockholm (Fig. 1). During recent years the Baltic has experienced large-scale water quality degradation. The water quality depends on the quality of runoff from sur-rounding drainage areas. The nutritional state of the water and risks for toxic algae bloom are determined by the nitrogen and phosphorous con-tent. Due to the substantial changes in land use, atmospheric deposition, and waste water discharge over the last decades it would be reasonable to

12 R. Berndtsson, J. Olsson, B. Sivakumar, and K. Jinno

believe that total pollutional load from nutrients has increased significantly. Contrary to this general belief, recent research has shown that the total riv-erine load of nitrogen and phospho-rous has been fairly constant since about 1970 (Stålnacke et al., 1999). They showed that riverine loads of phosphorous and nitrogen to the Baltic Sea by far exceeded the input from other sources, i.e., atmospheric deposition, direct emissions from cit-ies and industries along the Baltic Sea coast, and nitrogen fixation by marine algae. They consequently showed that there exists a strong correlation be-tween river runoff and total nutrient load to the Baltic Sea and that varia-tion in this load was largely due to natural variation in runoff. The water quality depends on the quality of runoff from surrounding drainage areas but critically also on

the so called Major Baltic Inflows that freshen the Baltic Sea water with influx of saline and oxygen-rich water from the North Sea depending on specific sequences of winds and atmosphere pressure (Matthäus and Schinke, 1994; Lass and Matthäus, 1996). These short-lived (in the order of one to three weeks) freshening episodes are related to the North Atlantic Oscillation (NAO). The NAO is of major importance for precipitation conditions over Scandinavia, especially winter precipitation (e.g., Uvo and Berndtsson, 2002; Uvo, 2003). The NAO is an atmospheric oscillation that relates the atmospheric pressure at Iceland and the Azores (e.g., Hurell, 1995; Reeds, 1999; Kushnir, 1999). The effects of this oscillation directly influence the meteorological and climatic conditions in Scandinavia. The NAO is, however, a part of the Earth´s atmosphere that is generally consid-ered to be part of a chaotic system (Lorenz, 1963; Shukla, 1998). As such, it is reasonable to believe that also sub-systems of Earth´s atmosphere like the NAO will be chaotic. Indeed, several researchers during recent years have found this to be true (e.g., Morton, 1998). According to this theory, it is

Figure 1. Principal Baltic Sea drainage basins used in the analyses. The Baltic Proper is shown in lighter grey as it was not included in this study (after Graham et al., 2009).


impossible to predict the exact time evolution of the NAO, or for that mat-ter precipitation, over more than a time steps into the future (Morton, 1998). Consequently, rainfall-runoff processes will also, at a regional scale where NAO is essential, follow chaotic characteristics. Long-term pre-dictions of climate and runoff become excluded by chaotic definition. Repeated short-term forecasts, however, are possible based on information about the chaotic system. The tool to resolve the chaotic system and the theoretical background for this is called dynamical systems theory (e.g., Abarbanel, 1996). According to the above, major inflow of nutrients to the Baltic Sea appears to be correlated to the natural discharge from surrounding catch-ment area and the driver of precipitation and runoff appears to be a chaotic atmosphere. The general climate and temperature development determines the atmospheric flow. According to this reasoning a physical relationship exists between the climate and the environmental state of the Baltic Sea. Accordingly, the objective of this paper is to discuss nonlinear cause-effect relationships of climatic observables (temperature and pre-cipitation) and total riverine nutrient loading (phosphorous and nitrogen transport). We exemplify with observations of temperature back to the 18th century and model simulations of temperature, precipitation and runoff during the last millenium to the Baltic Sea. A dynamical sys-tems approach is used to discuss nonlinear relationships between these variables.

Chaotic Climate?Solar-climatic relationships are a much debated issue (e.g., Willett, 1974; Muir, 1977; Colebrook, 1977; Pittock, 1978; Reid, 1987; Salby and Shea, 1991). Many investigations have utilized the sunspot number as an indi-cation of solar activity (Labitzke, 1987; Barnston and Livezey, 1989; van Loon and Labitzke, 1988). However, recent research indicates that the sun-spot cycle length (SCL) may be a more important variable to use when studying solar-climatic relationships (Friis-Christensen and Lassen, 1991; Kelly and Wigley, 1992; Butler, 1994). The SCL is defined as the time in years between the cycles of maximum (or minimum) values in the observed sunspot time series (e.g., Matsumoto et al., 1996a; 1996b). The SCL has been shown to vary with solar activity so that high activity implies short cycles and low activity long cycles (Friis-Christensen and Lassen, 1991).


Consequently, the SCL may be said to give a measure of the long-term accumulated energy output of the Sun. Hence, it is reasonable to expect an inverse relationship between SCL and temperature. If a significant solar-climatic relationship exists it may be utilized to improve the prediction accuracy for future temperature changes and to improve the understanding of how human activities may influence future climate. Several studies during recent years have indicated nonlinear and chaotic properties for sunspots and solar activity in general (Ruzmaikin, 1981; Zel-dovich and Ruzmaikin, 1983; Gilman, 1986; Kurths and Herzel, 1987; Weiss, 1988; Feynman and Gabriel, 1990; Mundt et al., 1991; Berndtsson et al., 1994; Jinno et al., 1995). Mundt et al., (1991) noted that one reason why models based on periodic behavior fail to predict sunspot time series accu-rately, may be the nonlinear behavior of the time series. Recently, studies that consider the chaotic properties of the Sun’s behavior have indicated that better predictions can be made using developments within chaos theory (Kurths and Herzel 1987; Weiss 1988; Mundt et al. 1991). As mentioned above, it is important to establish causal relationships be-tween climate and other readily observable variables. Friis-Christensen and Lassen (1991) and Kelly and Wigley (1992) both found a link between SCL and land air temperature. Butler (1994) also found a significant relationship between SCL and land air temperature at a point. In line with this, Fig. 2 shows the co-variation between SCL and mean monthly temperature for Lund, Sweden, for 238 years (1753–1991). According to the figure there

are obvious similarities between the two graphs. The linear correlation be-tween SCL and mean monthly tem-perature is about 0.6 for data after 1860 when temperature measurements were standardized. It may however be more important to compare the nonlinear co-variation be-tween SCL and temperature. This is especially important if chaos is at hand. Consequently, Fig. 3 shows attractors for SCL and mean monthly temperature with same data is in Fig. 2. The figure presents a rather striking comparison between cold and warm periods and corresponding long and short SCLs.

Figure 2. Co-variation between SCL and mean monthly temperature in Lund, Sweden (after Matsumoto et al., 1996a).


The information in Fig. 3 can be used for prediction purposes. Figure 4 shows a comparison between 6- and 12-month ahead prediction of mean temperature using local polynomials (Abarbanel, 1996). It is seen that espe-cially for 6-month ahead prediction the results appear quite reasonable.

Chaotic Runoff?A common problem involved in dynamic analyses is the necessity for long time series (e.g., Sivakumar, 2000; 2004, Sivakumar et al., 2002). A possible way to circumference this problem is to extend observations by modeling.

Figure 3. Nonlinear co-variation between SCL and mean annual temperature in Lund, Sweden (after Matsumoto et al., 1996a).

Figure 4. Real-time 6- and 12-month ahead prediction of average monthly temperature using local polynomials, data between 1860–1910 (after Berndtsson et al., 2001).


Runoff observations for the Baltic Sea exist back to about the 1920s. Daily runoff simulations based on observed precipitation and a distributed model exist from about 1980–2005 (Graham et al., 2009). To extend these observations and simulations back to about 1000 AD a ‘paleosimulation’ covering the Baltic Sea drainage basin and the surrounding areas was per-formed to obtain annual temperature, precipitation, and runoff. Tempera-ture and precipitation were simulated by the coupled atmosphere-ocean global climate model ECHO-G (Legutke and Voss, 1999). The model is based on three major variables; a) concentrations of CO2 and CH4, b) vol-canic and solar radiative forcing, and c) sunspot observations. Tempera-ture and precipitation was then downscaled using the regional climate model RCA3 (Kjellström et al., 2005) coupled with the FLAKE lake model (Mironov, 2007). The well-known conceptual HBV hydrologic model (e.g., Lindström et al., 1997) was used to reconstruct river flow to the Baltic Sea. Graham (1999) calibrated the HBV model for daily obser-vations. The outcome was daily temperature, precipitation and runoff for three periods between years 1000 and 1929 (1000–1199, 1551–1749, 1751–

1929; Graham, 2004; Graham et al., 2007). These simulated data are analyzed in this paper. Figure 1 shows the coverage of the simulations. The southern part of the Baltic Basin was not covered due to lacking RCA3 model coverage. Figure 5 shows (bottom to top) the simulated annual temperature, precip-itation, and runoff series for the peri-ods 1000–1199, 1551–1749, and 1751–1929.A large variation is obvious from the graphs for all three variables. However, from the 30-year average (shown in the figure with thick lines), all three variables also appear to fol-low a quasi-periodic behavior. While an increasing trend is noticeable for temperature and precipitation during the later periods, no pronounced linear trend is evident for runoff. There is a

Figure 5. Simulated annual temperature, pre-cipitation, and runoff from the Baltic Basin. Thick line shows 30-year average (after Bern-dtsson et al., 2009).


general linear correlation between annual temperature and precipita-tion equal to 0.53, and between pre-cipitation and runoff equal to 0.77; however, the correlation between temperature and runoff is as low as 0.30. However, since we may expect

a general nonlinear relationship between, e.g., temperature and runoff, the linear correlation is not so interesting. Instead we are looking for nonlinear relationships. Using the average temperature and average runoff according to Fig. 5 we can construct attractors (5-year time lag) to decipher the non-linear relationship between these two variables. Figure 6 shows that a warm period in general means a larger runoff and a cold period means smaller runoff. According to the figure about 2 degrees warmer climate means about 15 % larger runoff. The information in Fig. 6 could be used in uni-variate prediction schemes as shown for temperature in Fig. 4. However, also prediction schemes utilizing the multivariate nonlinear relationship could be used. Figure 7 shows an example of multivariate nonlinear rela-tionship between average annual temperature and future average annual runoff (5 years ahead). According to the above there appears to be quantifi-able nonlinear relationships between average temperature and average run-off. The temperature variation appears to, at least in part, to be governed by

Figure 6. Nonlinear co-variation between annual temperature and runoff for data in Fig. 5 (after Berndtsson et al., 2009).

Figure 7. Nonlinear relationship between average annual temperature and future average annual runoff (5 years ahead; after Berndtsson et al., 2009).


changes in the incoming solar energy. For the Baltic Sea it was shown by Stålnacke et al. (1999) that strong correlation exists between river runoff and total nutrient load and that variation in this load was largely due to natural variation in runoff (Fig. 8 and 9). Consequently, this reasoning then indicates that the future nutrient load to the Baltic Sea and thus also the environmental state would be possible to predict by, e.g., using temperature only.

Conclusion and DiscussionIn the above we have argued that climate forcing on temperature, precipita-tion, and runoff display chaotic characteristics. Good results using dynam-ical univariate prediction scheme for average monthly 6- and 12-month ahead temperature confirms this assumption. Using validated model simu-lations of temperature, precipitation, and runoff to the Baltic Sea from 1000 AD shows that warm and cold periods, respectively, result in correspond-ing larger and smaller runoff. Since the main total nutrient loading to the Baltic Sea is riverine phosphorous and nitrogen following the natural river discharge variation, a strong correlation exists between natural inflow and riverine discharge. Due to this it is likely that univariate and multivariate dynamic prediction schemes would work well to predict the future envi-ronmental state of the Baltic Sea. Our future research will show the out-come of this.

Figure 8. Annual riverine nitrogen load to the area in Fig 1. White and black staples are inor-ganic and organic nitrogen, respectively (after Stålnacke et al., 1999).

Figure 9. Annual riverine phosphorous load to the area in Fig 1. White and black staples are inorganic and other phosphorous, respectively (after Stålnacke et al., 1999).


AcknowledgementsThe first author acknowledges the funding support by the ITP-JSPS and the MECW project at the Center for Middle Eastern Studies for presenting this study. Parts of this paper was also presented at the International Sym-posium on Earth Science and Technology 2009, Fukuoka, Japan.

ReferencesAbarbanel, H D I, Analysis of observed chaotic data, Springer, New York (1996).Barnston, A G, and Livezey, R E, A closer look at the effect of the 11-year solar cycle and

the quasi-biennial oscillation on northern hemisphere 700 mbar height and extra-tropical North American surface temperature, J. Clim, 2, 1295–1313 (1989).

Berndtsson, R, Jinno, K, Kawamura, A, Olsson, J, and Xu, S, Dynamical systems theory applied to long-term temperature and precipitation time series, Trends in Hydrol. 1, 291–297 (1994).

Berndtsson, R, Uvo, C B, Matsumoto, M, Jinno, K, Kawamura, A, Xu, S, and Olsson, J, Solar-climatic relationship and implications for hydrology, Nord. Hydrol. 32, 65–84 (2001).

Berndtsson, R, Sivakumar, B, Olsson, J, and Graham P, Climate change and its effects on regional hydrology: A case study for the Baltic Sea drainage basin, Proc. MODSIM Conf. Cairns, Australia, 13–17 July, Water and Climate Change: Impacts, Adapta-tion and Mitigation (2009).

Butler, C J, Armagh observatory, 1844–1992, and the length of the sunspot cycle, Solar Phys. 152, 35–42 (1994).

Colebrook, J M, Reply on Muir (1977), Nature, 266, 476 (1977).Feynman, J, and Gabriel, S B, Period and phase of the 88-year solar cycle and the Maun-

der minimum: evidence for a chaotic sun, Solar Phys. 127, 393–403 (1990).Friis-Christensen, E, and Lassen, K, Length of the solar cycle: an indicator of solar activ-

ity closely associated with climate, Science, 254, 698–700 (1991).Gilman, P A, The solar dynamo: observations and theories of solar convection, global

circulation, and magnetic fields, In: P. A. Sturrock (ed.), Physics of the Sun, Vol. I, pp. 95–160, D. Reidel Publ. Co., Mass. (1986).

Graham, L P, Modeling runoff to the Baltic Sea, Ambio, 28, 328–334 (1999).Graham, L P, Climate change effects on river flow to the Baltic Sea, Ambio, 33, 235–241

(2004).Graham, L P, Hagemann, S, Jaun, S, and Beniston, M, On interpreting hydrological

change from regional climate models, Climate Change, 81, 97–122 (2007).Graham, P, Olsson, J, Kjellström, E, Rosberg, J, Hellström, S-S, and Berndtsson, R,

Simulating river flow to the Baltic Sea from climate simulations over the past millen-nium, Boreal Env. Res., 14, 173–182 (2009).

Hurrell, J W, Decadal trends in the North Atlantic Oscillation: regional temperatures and precipitation, Science, 269, 676–679 (1995).

Jinno, K, Xu, S, Berndtsson, R, Kawamura, A, and Matsumoto, M, Prediction of sun-


spots using reconstructed chaotic system equations, J. Geophys. Res. 100, 14773–14781 (1995).

Kelly, P M, and Wigley, T M L, Solar cycle length, greenhouse forcing and global climate, Nature, 360, 328–330 (1992).

Kjellström, E, Bärring, L, Gollvik, S, Hansson, U, Jones, C, Samuelsson, P, Rummukai-nen, M, Ullerstig, A, Willén, U, and Wyser, K, A 140-year simulation of European climate with the new version of the Rossby Centre regional atmospheric climate model (RCA3), Reports Meteorology and Climatology, 108, SMHI, SE-60176 Norr-köping, Sweden, 54 pp. (2005).

Kurths, J, and Herzel, H, An attractor in a solar time series, Physica D, 25, 165–172 (1987).

Kushnir, Y, Europe’s winter prospects, Nature, 398, 289–291 (1999).Labitzke, K, Sunspots, the QBO, and the stratospheric temperature in the north polar

region, Geophys. Res. Lett., 14, 535–537 (1987).Lass, H U and Matthäus, W, On temporal wind variations forcing salt water inflows into

Baltic Sea, Tellus, 48A, 663–671 (1996).Legutke, S, and Voss, R, The Hamburg Atmosphere-Ocean coupled circulation model

ECHO-G, Technical Report 18, DKRZ, Hamburg, 62 pp. (1999).Lindström, G, Johansson, B, Persson, M, Gardelin, M, and Bergström, S, Development

and test of the distributed HBV-96 model, J. Hydrol. 201, 272–288, (1997).Lorenz, E N, Deterministic nonperiodic flow, J. Atmos. Sci., 200, 130–141 (1963).Matsumoto, M, Berndtsson, R, Kawamura, A, and Jinno, K, A relationship between

sunspot cycle length and temperature in Lund, Sweden, J. Hydraul. Eng., JSCE, 40, 365–370 (in Japanese with English abstract; 1996a).

Matsumoto, M, Kawamura, A, Jinno, K, Berndtsson, R, and Xu, S, Prediction of month-ly temperature time series using reconstructed chaotic system equations, Proc. Intern. Conf. Water Resour. & Environm. Res. 21st Cent., Kyoto, Oct. 29–31, Vol. 1. (1996b).

Matthäus, W and Schinke, H, Mean atmospheric circulation patterns associated with Major Baltic Inflows. Germ. J. Hydrogr., 46, 321–339 (1994).

Mironov, D V, Parameterization of lakes in numerical weather prediction. Part 1: De-scription of a lake model, German Weather Service, Offenbach am Main, Germany, 41 pp. (2007).

Morton, O, The North Atlantic´s El Nino, New Scientist, 31, 22–27 (1998).Muir, M S, Possible solar control of North Atlantic oceanic climate, Nature, 266, 475–476

(1977).Mundt, M D, Maguire II, W B, and Chase, R R P, Chaos in the sunspot cycle: analysis

and prediction, J. Geophys. Res., 96, 1705–1716 (1991).Pittock, A B, A critical look at long-term sun-weather relationships, Rev. Geophys.

Space Phys., 16, 400–420 (1978).Reeds, J, Ocean Review, Geographical, 71, 72–74 (1999).Reid, G C, Influence of solar variability on global sea surface temperature, Nature, 329,

142–143 (1987).Ruzmaikin, A A, The solar cycle as a strange attractor, Comments on Astrophysics, 9,

85–93 (1981).


Salby, M L, and Shea, D E, Correlations between solar activity and the atmosphere: an unphysical explanation, J. Geophys. Res., 96, 22579–22595, (1991).

Shukla, J, Predictability in the midst of chaos: a scientific basis for climate forecasting, Science, 282, 728–731 (1998).

Sivakumar, B, Chaos theory in hydrology: important issues and interpretations, J. Hy-drol., 227, 1–20 (2000).

Sivakumar, B, Chaos theory in geophysics: past, present, and future, Chaos Solitons Fractals, 19, 441–462 (2004).

Sivakumar, B, Persson, M, Berndtsson, R, Uvo, C B, Is correlation dimension a reliable indicator of low-dimensional chaos in short hydrological time series? Water Resour. Res. 38, doi: 10.1029/2001WR000333 (2002).

Stålnacke, P, Grimvall, A, Sundblad, K, and Tonderski, A, Estimation of riverine loads of nitrogen and phosphorous to the Baltic Sea, 1970–1993, Environm. Monit. Ass., 58, 173–200. (1999).

Uvo, C B, Regionalization of Northern Europe winter precipitation based on its rela-tionship with the North Atlantic Oscillation, Intern. J. Climatol., 23, 1185–1194 (2003).

Uvo, C B and Berndtsson, R, North Atlantic Oscillation; a climatic indicator to predict hydropower availability in Scandinavia, Nord. Hydrol., 33, 415–424 (2002).

van Loon, H, and Labitzke, K, Association between the 11-year solar cycle, the QBO, and the atmosphere, II, Surface and the 700 mb in the Northern Hemisphere in win-ter, J. Clim., 1, 905–920 (1988).

Weiss, N, O, Is the solar cycle an example of deterministic chaos?, In: F. R. Stephenson and A. W. Wolfendale, Secular Solar and Geomagnetic Variations in the Last 10,000 Years, pp. 69–78, Kluwer, Boston (1988).

Willett, H, C, Recent statistical evidence in support of the predictive significance of solar-climatic cycles, Mon. Weath. Rev., 102, 679–686 (1974).

Zeldovich, Y B, and Ruzmaikin, A A, Dynamo problems in astrophysics, In: R. A. Syunyaev (ed.), Soviet Sci. Rev., Section E, pp. 333–383, Harwood, New York (1983).

dynamic links between climate and environmental change · ter precipitation, over more than a time...

Documents