Diagnostic study on warming mechanism of spring water temperature based on field observations and numerical simulation : a case study of Masugatanoike spring , Tokyo , Japan

Air temperature rise in Tokyo is distinctively large after 1980. Reflecting this feature, water temperature at Masugatanoike, a spring in Tokyo that stands a foot of terrace scarp that the height is 14 m, rose after the end of 1980s. The water temperature began to rise 4–7 years after the air temperature rose, showing a statistically significant correlation at the 5% level. This warming water must be explained by downward thermal conduction because there are no hot springs, subways, or major sewers around Masugatanoike spring. In this study, we first solved the surface energy balance in Tokyo from 1951 to 2009 to estimate the daily mean ground surface temperature. Next, we calculated the thermal conduction from the ground surface to a depth of 16 m. The initial condition was optimized so that root mean square error of the observed and calculated temperatures at a depth of 14 m from 1976 to 2009 was minimized. We found that 4–8 years were necessary until the effects of ground surface temperature reached a depth of 14 m after 1975. Namely, we demonstrated that downward thermal conduction is responsible for the above-mentioned lag relation, which was found in the observation.


INTRODUCTION
Global warming has attracted much attention because it affects present and future climate.Moreover, urban areas are influenced by heat islands.Both of them influence subsurface temperatures in the urban area which has been studied for a long time (see Taniguchi et al., 2009 and references therein).In this regard, water temperatures of many springs in Tokyo have been rising in recent 20 years (Narumiya et al., 2006).Among them, Ogura (2000) conducted long-term observations of water temperature at Masugatanoike spring (Figure 1).
According to Ogura (2000), water temperature at Masugatanoike spring rose about 0.8°C during 1987-1997, by delaying air temperature (Figure 2).The lag correlation coefficients were largest and statistically significant for water temperature lagging air temperature by 4-7 years (Figure 3).We therefore hypothesize that the effect of global warming and heat islands has appeared in spring water temperature with some delay, however, this is only speculation.
This phenomenon must be mainly explained by thermal conduction from the ground surface because there are no hot springs, subways, or major sewers around Masugatanoike spring.It is generally regarded that the groundwater temperature is thermally in equilibrium with soil temperature, therefore, the objective of this study is to demonstrate that the thermal conduction is responsible for the warming of water temperature at Masugatanoike spring (Figures 2 and 3), based on simple but realistic assumptions and calculations.

STUDY AREA
Masugatanoike spring is located about 25 km west of central Tokyo (around 35.69N, 139.47E; Figure 1).It stands on a foot of a terrace scarp that the height is 14 m between Musashino terrace and Tachikawa terrace, both covered by permeable volcanic ash soil (Kanto loam) that is around 5-10 m thick (Kaizuka, 1979).Below Kanto loam, a sand and gravel layer holds shallow partly confined aquifers from which Masugatanoike spring drains.
Masugatanoike spring is located in the bedroom suburb of central Tokyo.According to the topographical maps issued by Geospatial Information Authority of Japan, along with the estimated drainage area of Masugatanoike spring (Tsushima et al., 2008), original coniferous forests at Musashino terrace around Masugatanoike spring were converted to urbanized land use at least in 1952, then the urbanization was gradually progressing.This land use change certainly affects the interannual variability of subsurface temperatures, however we did not incorporate it directly into the calculations.Instead, we will qualitatively discuss this effect in "DISCUSSION".

Calculation of thermal conduction
The equation of thermal conduction, usually expressed one-dimensionally, is described as follows, with z being positive downwards. .
( 1 ) Here, T is soil temperature (°C or K), t is time (second), ), ρ G is soil density (kg m −3 ), respectively.We solved Equation (1) from ground surface to a depth of 16 m with a 0.1 m interval and time step of 2 × 10 −4 year (about two hours) to satisfy the Courant-Friedrichs-Lewy condition.We supposed that the effect of ground surface temperature did not exceed a depth of 16 m.This setting is certified because the upper limit of the isothermal stratum around Tokyo is about a depth of 12 m (Kiuchi, 1950).The method for estimating ground surface temperature is explained in the next subsection.
We adopted the thermal diffusivity of 2.4 × 10 −7 m 2 s −1 used in Genchi et al. (1998) which calculated thermal conduction at Kanto loam.In this study, we did not take into account the thermal advection of ground water because we judged from Taniguchi et al. (1999) that the effect of downward water flux on subsurface temperatures is negligible at a depth of 14 m.We did not consider the effect of soil moisture on the heat transport either, following such experiment conducted in Tokyo (e.g., Genchi et al., 1998).
The deeper part of Musashino terrace consists of a sand and gravel layer (Kaizuka, 1979), whose thermal diffusivity is 6.6 × 10 −7 m 2 s −1 ("wet sand and clay" in Genchi et al., 1998).Namely, it is possible that the heat transfer of the deeper layer is faster than the shallower layer.We will also   discuss this effect in "DISCUSSION".
We estimated the soil temperatures at a depth of 14 m to compare with observed ones after 1976.The observations for 1976-1997 were derived from Figure 2, while those for 1998-2009 were based on Narumiya et al. (2006) and its continuance which observed water temperatures twice a year in the dry/rainy seasons.They were simply averaged to give annual mean temperature.The initial value of soil temperature at each 0.1 m layer was optimized to minimize the root mean square error of the calculated and observed temperatures, with the initial value being positive to satisfy the thermal diffusivity selected.We conducted this calculation from 1951 to 2009 (see next subsection) and analyzed the period after 1975 so that the effect of initial soil temperatures was minor.Note that this experiment did not investigate the equilibrium/average state, but captured the warming stage of soil temperatures.

Estimation of the surface temperature
We estimated daily mean surface temperatures by solving the daily mean surface energy balance, then, we temporally resolved ground surface temperatures to 2 × 10 −4 year's one by considering its diurnal variation.In a time scale longer than a day, air temperature and ground surface temperature do not have lag relation, i.e., both are high (low) in summer (winter).In this case, the relation between air temperature and spring water temperature (Figure 2) is almost identical to that between the ground surface temperature and soil temperature at a depth of 14 m.We therefore analyzed the relation of the latter two.
Because the observed variables at AMeDAS Fuchu are insufficient for calculating the surface energy balance, we calculated it using daily data of Tokyo District Meteorological Observatory (Figure 1).The input daily data were surface air pressure, mean, maximum, and minimum air temperatures, vapor pressure, wind speed, downward shortwave radiation, and precipitation.According to Kondo et al. (1992b), errors arising from calculating surface energy balance are smaller than those of atmospheric forcing, i.e., we can use these data of a relatively far station, such as 25 km apart from central Tokyo (Figure 1).
We set the period of calculation for 1951-2009 by trial and error, partly because we can easily obtain daily data from 1961 at this observatory (http://www.data.jma.go.jp/ obd/stats/etrn/index.php).In addition, we digitalized the printed data of this station from 1951 to 1960 to minimize the effect of initial values of soil temperatures.
For calculations, we followed the methods in Kondo et al. (1992a) and Kondo and Nakazono (1993).They calculated the surface energy balance separately according to weather conditions (clear days, lightly rainy days, and heavy rainy days), provided that the surface is covered with trees which needs leaf area index (LAI), albedo, and surface moisture availability (Kondo et al., 1992a).In this experiment, we modified LAI, albedo, and surface moisture availability for those of asphalt (0.7 m 2 m −2 , 0.1, and 0.0, respectively, Kondo and Nakazono, 1993).We did not consider the interannual variability of land use change, which will be discussed in "DISCUSSION".
The output daily mean data were sensible heat flux, latent heat flux, interception loss, and ground surface temperature.The daily mean ground heat flux was assumed to be zero in this calculation.Instead, we considered the diurnal variation of the ground surface temperature.Kondo (1992) proposed a method to estimate the diurnal variation of the ground surface temperature on a fine weather day.Concretely, the hourly data of downward shortwave radiation and air temperature at Tokyo District Meteorological Observatory, approximated by sinusoidal function, were given to estimate an amplitude and a phase of diurnal change of ground surface temperature analytically, provided that downward long-wave radiation was constant within a day.Note that the daily mean, maximum and minimum air temperatures used for the surface energy balance were not directly related to this calculation.Here, the exchange coefficient (C H U: 0.01 m s −1 ) and the thermal parameter of soil (C G ρ G λ G : 2 × 10 6 J 2 s −1 K −2 m −4 ) were fixed considering typical meteorological conditions.Temporal resolution of the atmospheric turbidity, necessary for estimating downward short-wave radiation was limited to a month (Kondo and Watanabe, 1991), so that we conducted this calculation for each month.We linearly resolved the obtained daily mean ground surface temperature to 2 × 10 −4 year's one with the maximum and minimum appearing at 14:00 and 05:00 local standard time, respectively.

RESULTS
We checked the seasonal change and interannual variability of temperatures at the ground surface, depths of 7 m and 14 m during 1951-2009.A visual inspection revealed that initial conditions fairly affected the results at least for 20-25 years, so that we showed the results after 1975 here (Figure 4).As is expected, seasonal change was large at the ground surface, i.e., from ca. −8 to 49°C within a year.In contrast, it was slightly (hardly) seen at a depth of 7 m (14 m).Soil temperatures at depths of 7 m and 14 m gradually rose during this period.
Figure 5 depicts a time-depth cross section of soil temperature during 1975-2009, along with the annual mean air temperature at Tokyo District Meteorological Observatory.From this figure, we found that the annual mean air temperature steadily increased during this period with highfrequency fluctuations, while cyclic variation of one year prevailed in the subsurface temperature in the shallower layers.We also saw some contours penetrated into the deeper layers.
Here, we pay attention to the contours above 16.0°C, which are traceable from the ground surface to a depth of 16 m in Figure 5b.For example, the contour of 16.0°C which appeared on the ground in 1978, reached to a depth of 14 m in 1986.The time necessary for the penetration was 8 years (Table I).From Table I, we can perceive that four to eight years are necessary for the contours of 16.0-17.0°Cto penetrate from the ground surface to a depth of 14 m.
Considering that air temperature and ground surface temperature are synchronized in the time scale longer than a day, we think Figure 5 and Table I do not contradict that a 4-7 year lag relation was found between observed air temperature and water temperature (Figures 2 and 3).Namely, we demonstrated that thermal conduction was responsible for the lag relation portrayed in Figures 2 and 3.

DISCUSSION
The calculation scheme adopted in this study is based on the surface energy balance of forest canopy (Kondo et al., 1992a), so that we cannot directly substitute the surface temperature of the forest canopy into Equation (1).To overcome this defect, we should introduce more sophisticated land-surface scheme.Instead, we give some qualitative consideration how land use change affects the interannual variability of subsurface temperatures.
Around Masugatanoike spring, original coniferous forests at Musashino terrace were converted to urbanized land use at least in 1952, then the urbanization was gradually progressing (see "INTRODUCTION").In comparison with the case of asphalt, ground surface temperature of natural land use (such as coniferous forest) will have a smaller amplitude both diurnally and seasonally.This diminishes and delays the warming of subsurface temperatures.On the other hand, Oguchi et al. (2008) displayed that the upper 8 m layer around Masugatanoike is composed by Kanto loam, while the deeper layers consist of gravel, sand, clay and silt whose thermal diffusivity are larger than that of Kanto loam (Genchi et al., 1998).Also, Oguchi et al. (2008) revealed that groundwater level in the deeper layer shows seasonal fluctuation that repeats saturated/unsaturated condition.It is expected that the thermal conduction in the deeper layer will be faster than our experiment.
In summary, we think that the effects of land use change and vertical distribution of the thermal diffusivity will compensate each other, indicating that our experimental settings will be in the midst of the actual situation.Nevertheless, it is sure that the thermal conduction Table I.Detailed information related to the contours penetrating from the ground surface to a depth of 14 m in Figure 5b Contour Appearance at the ground surface (year) Arrival at a depth of 14 m (year)

CONCLUSION
Giving simple but realistic settings, we demonstrated what we imagined, i.e., the thermal conduction accompanied with the increase of surface air temperature was responsible for the lag relation between observed air temperature and water temperature at Masugatanoike spring.Still, there is room for the improvement.Now we are analyzing the interannual variability of land use change using satellite images.Also, the effect of seasonal variation of ground water level should be taken into account.We will sophisticate our calculation scheme in the near future.

Figure 1 .
Figure 1.Locations of Masugatanoike spring, AMeDAS Fuchu, and Tokyo District Meteorological Observatory.Latitudes and longitudes in the brackets represent the position of the middle panel.Topographic contours are drawn every 2 m in the lower panel.

Figure 2 .
Figure 2. Interannual variability of annual mean water temperature at Masugatanoike spring and annual mean air temperature at AMeDAS Fuchu.Modified after Figure 5 of Ogura (2000) with the permission of the Japanese Society of Limnology which holds the copyright of the original figure.

Figure 3 .
Figure 3. Lag relation of Figure 2. The x-axis shows the preceding years of air temperature.The correlation coefficients at 4-7 years are statistically significant at the 5% level.

Figure 5 .
Figure 5. Interannual variability of annual mean air temparature at Tokyo District Meteorological Observatory, and (b) time-depth cross section of soil temperature from 1975 to 2009.Contours are drawn every 0.5°C.