Determination of Solar Cycle and Natural Climate Variation using both Surface Air/Soil Temperature and Thermal Diffusion Model Xiquan Dong (Atmospheric Sciences) and Will Gosnold (Geology and Geological Engineering), University of North Dakota ; This research is supported by NSF ATM Goals: Use daily surface air and soil temperatures over the Northern Great Plains during the and a 2-D, finite-difference, conductive thermal diffusion model to (1) detect the solar cycle, and (2) determine natural climate variation during a 11-yr solar cycle. Data sets and Time Period were obtained from High Plains Regional Climate Center (HPRCC) in Lincoln, NE from May 19, 1981 to December 31, Daily air and soil temperatures over KS, NE, SD and ND were obtained from High Plains Regional Climate Center (HPRCC) in Lincoln, NE from May 19, 1981 to December 31, A least-squares fit of the first five years of data is performed to determine the initial model temperature. To simplify the calculation so it has a 0 o C starting point, the initial temperature was subtracted from the original data as shown in Figure 3 (Figure 4 for soil temperature). Results: Conclusions 1)Solar cycle From Figures 7 and 8, we can see that the temperature variations match the variations of total solar irradiance. This indicates that we can predict 11-yr solar cycle using both the surface air/soil temperatures as forcing signals in our thermal diffusion model. We will apply this method to reconstruct longer period of solar cycles when thermometer temperature data are available (back to year 1895 at 2) Natural climate variation during a 11-yr cycle Based on Fig. 7, we have following conclusions during a 11-yr solar cycle: KS NE SD ND  T at 10 m o C  T at sfc 0.42, 0.70, o C The natural climate variation over the NGP region ranges from 0.42 to 0.94 o C during a 11-yr solar cycle. Fig. 2. Reconstructed solar irradiance (Lean et al. 2000, 2004, available at The GHCN global temperature data were downloaded from NCDC webpage. The GHCN temperature anomaly generally increases with increased total solar irradiance during the period, but its interannual variability does not correlate with the solar cycles. Thermal Diffusion Model: (1) A 2-D, finite-difference, conductive heat flow model was used with an initial condition T(x, 0) = 0 and boundary conditions of T(0, t) = the daily air/soil temperatures. (2) The output of the model is a time series matrix of temperature vs. depth (Fig. 5). The daily air/soil temperatures were averaged to compile a single record for each state (KS, NE, SD, ND) and these data were used as the forcing signals in the model. (3) The key to detection of the solar cycle and natural climate change is the filtering power of thermal diffusion which removes the short period signals (interannual) and retains the long period signals (decadal and centennial) in the upper 100 m. (4) The temperature at a depth of 10 m has a good signal-to-noise ratio and represents 53% of its surface amplitude for the period of a solar cycle. Fig. 1. Composite daily total solar irradiance (S 0 ) measured by satellites since The mean and standard deviation of S 0 are and 0.72 Wm -2 during the period, with about 0.1% (S max -S min = =1.35 Wm -2 ) variation during a 11- yr solar cycle. Fig. 3. Reconstructed daily air temperatures from a composite of 32 meteorological stations over the Northern Great Plains from Nebraska HPRCC. Fig. 5 Modeled diffusion of the GHCN air temperature anomaly. For approximately sinusoidal signals such as annual temperature and the solar cycle, the solution to the diffusion equation yields T = T 0 e –x√ω/2k cos(ωt - x√ω/2k) The signal amplitude at depth “x” is T 0 e –x√ω/2k and the phase retardation is –x√ω/2k where ω is angular frequency, k is diffusivity, t is time, and x is depth. Fig. 6. Daily temperatures for Grand Forks, ND from 1932 to 2004 shown as colors. Red is warm and blue is cool. The color patterns vaguely suggest pulses that may correspond with the solar cycle. However, analysis of a larger region than a single station is necessary to adequately assess any connection with the solar cycle. Fig.7. Time series of total solar irradiance (same as Fig. 1 with 3- yr shift) and the air temperature change at 10 m deep over KS, NE, SD, and ND (right y-axis). Motivation: A critical challenge in research on global climate change is separation of radiative forcing by anthropogenic “greenhouse” gases from radiative forcing due to natural climate variability which is closely associated with the length of the solar cycle. Solar irradiance at the top of atmosphere has been measured by satellites since 1978 (Fig. 1). However, the two measured solar cycles are too short to detect slow variations on multi-decadal time scales. Therefore, it is necessary to reconstruct longer time series of solar cycles and their influence on climate variability (Fig. 2). Fig. 4. Reconstructed daily soil temperatures from a composite of 32 meteorological stations over the Northern Great Plains from Nebraska HPRCC. Fig.8. Time series of total solar irradiance (same as Fig. 1 with 3- yr shift) and the soil temperature change at 10 m deep over KS, NE, SD, and ND (right y-axis). PP52A Jan 1 Dec 31