Evelise Bourlon Hugo Beltrami Environmental Earth Sciences Lab.

Worldwide recent ground surface warming pattern from borehole temperature profiles
Evelise Bourlon Hugo Beltrami Environmental Earth Sciences Lab. St Francis Xavier University Good afternoon. I will present a study done in collaboration with Hugo Beltrami and people of EESL lab at Saint FX university. It’s a broad scale analysis in space and time of the ground surface temperature variations in the Mid-latitude sector of the Northern hemisphere since 500 years using borehole data. International Workshop on “New and classical applications of Heat flow studies” Aachen (Germany), October 4-7, 2004

Outline Introduction From geothermal data to GST Worldwide database
Theory GST inversion Worldwide database GST reconstruction Gridding Latitudinal and hemispheric average Conclusions Reconstructions of the past temperature variations from the pre-industrial to the present periods provide information to characterize and quantify the natural and anthropogenic climate forcing. Many reconstructions based on proxy records such as tree rings or corals do not preserve low-frequency information. Here we present the result of a direct temperature-temperature study. We inferred ground surface temperature variations from borehole temperature logging. I will present the method and the data we used and then I will show you the reconstruction and its analysis.

From geothermal data to GST
Temperature (oC) T0 1y warming 10y cooling 100y Depth (m) Thermal front propagation timing In the case of thermal equilibrium of the Earth’s crust, a temperature-depth profile starts at the surface at the mean-annual ground temperature and increases steadily with depth. If the temperature at the upper boundary of the body is increased, additional heat propagates into the body causing a corresponding increase in temperature just below the surface. The depth to which equilibrium temperatures are perturbed in a given time is governed by the thermal diffusivity of the body. For typical rocks a thermal front propagates to about 20 m in one year, 50 m in 10 years, 160 m in 100 years, and 500 m in 1000 years. Thus the Earth’s ground temperature history over the last millennium is captured in the uppermost kilometer of the crust. Positive and negative subsurface temperature anomalies are associated with ground surface warming and cooling respectively. Thus, in absence of any other perturbation (land-use, snow cover, internal heat production), the temperature at given depth is the superposition of the quasi-equilibrium temperature and of the temperature perturbation caused by ground surface temperature variations. steady state 1000y

From geothermal data to GST
The temperature at depth z, T(z), is the superposition of the quasi-equilibrium temperature and of the temperature perturbation, Tt(z), caused by ground surface temperature variations: where T0 is a reference ground temperature, q0 is the surface heat flow density, R(z) is the thermal depth. If the past variations of ground surface temperature are modeled as a series of K-step temperature changes, then the subsurface temperature signals from each step change are superimposed, and the temperature perturbation at depth z is given by: where Tk are the ground surface temperatures, each value being an average over a period of time (tk-tk-1), erfc is the complementary error function and Tk are the times of the ground surface temperature changes. In the case of thermal equilibrium of the Earth’s crust, a temperature-depth profile starts at the surface at the mean-annual ground temperature and increases steadily with depth. If the temperature at the upper boundary of the body is increased, additional heat propagates into the body causing a corresponding increase in temperature just below the surface. The depth to which equilibrium temperatures are perturbed in a given time is governed by the thermal diffusivity of the body. For typical rocks a thermal front propagates to about 20 m in one year, 50 m in 10 years, 160 m in 100 years, and 500 m in 1000 years. Thus the Earth’s ground temperature history over the last millennium is captured in the uppermost kilometer of the crust. Positive and negative subsurface temperature anomalies are associated with ground surface warming and cooling respectively. Thus, in absence of any other perturbation (land-use, snow cover, internal heat production), the temperature at given depth is the superposition of the quasi-equilibrium temperature and of the temperature perturbation caused by ground surface temperature variations.

GST inversion Inversion of GST was performed with a singular value decomposition algorithm [Beltrami and Mareschal, 1992]. Parameters of this inversion scheme were keep identical at each location (eigenvalue cutoff=0.; thermal diffusivity=10-6m2s). The past variations of the ground surface temperature were modeled as a series of fifty years step changes. We used a singular value decomposition algorithm to invert the GST. It selects the components of the ground surface temperature history best represented in the underground signal. It has been proven to be very robust against noise. We keep the same inversion parameters at each site And we model the GST history as a series of 50 years steps. The GST changes are expressed as departures from the long-term mean at each location.

Number of boreholes per grid cell
Worldwide database Ground surface temperature (GST) histories over the last five centuries have been reconstructed based on temperature measurements from 558 boreholes from the International Heat Flow Commission. This data set contains 105 additional temperature logs than the data set used in Huang et al. (2000). All these boreholes are distributed in the 30º-60ºN temperate area. All of them are deeper than 200km and we cut the first 30 m to get rid of annual effects. There is an average of 5 boreholes per 500 by 500 km grid cell. Number of boreholes per grid cell 778 boreholes from the International Heat Flow Commission.

Worldwide database 200m<depth<600m
Ground surface temperature (GST) histories over the last five centuries have been reconstructed based on temperature measurements from 558 boreholes from the International Heat Flow Commission. This data set contains 105 additional temperature logs than the data set used in Huang et al. (2000). All these boreholes are distributed in the 30º-60ºN temperate area. All of them are deeper than 200km and we cut the first 30 m to get rid of annual effects. There is an average of 5 boreholes per 500 by 500 km grid cell. 200m<depth<600m 558 boreholes from the Northern Hemisphere.

GST gridding 2 major problems arise in data mapping and average calculation when very sparse data: Projection distortion in the mapping: We need to account for the shrinking size of the geographical cells towards the poles. The gridding procedure was done on a kilometric grid then transferred to a geographical grid using a sinusoidal projection. Geographical aggregation: We want to avoid giving too much representation to areas in the Northern Hemisphere containing large number of boreholes (Canada, for example).  We first filter the data on a (1000x1000km) cell grid. A block average method has been applied to compute a mean location and the L2 norm average t value in each cell.  Then a surface gridding algorithm produces a 15° gridded data set from the unevenly spaced data using a tension parameter k=0.25 yielding to a near minimal curvature surface.  We let edges at 20°S and 70°N of latitude be free. The grid is periodic in 360° of longitude. In order to avoid giving too much representation to areas in the northern hemisphere containing large number of boreholes (Canada for example), we used a gridding procedure for display purposes. A block average method has been applied to compute a mean location and the L2 norm average t value in each cell. This is to suppress redundant data and avoid spatial aliasing. Then a surface gridding algorithm produces a 15’ gridded data set To account for the shrinking size of the geographical cells towards the poles, the gridding procedure was done on a kilometric grid then transferred to a geographical grid using a sinusoidal projection. Because of the sparse spatial distribution of the boreholes, we used an (remove ”different”) averaging technique to compute the ground surface temperature history rather than a simple arithmetic average. The arithmetic average give excessive weight to areas of high borehole density. we reassess the continental northern hemisphere average using a kilometric gridding instead of geographic aggregation. Thus, cells are of the same size and no area-weighting is required. Borehole locations were first converted into kilometer units using a sinusoidal projection relative to (0°N, 0°W). Temperature data were average on 500 km × 500 km cell to avoid spatial aliasing and suppress redundancy. Grid size effects, however, are not important on the determination of the northern hemisphere average (Pollack and Smerdon , 2004). To avoid that some latitudes (e.g. Canadian latitudes) containing many filled cells distort the hemispheric representation, we give the same weight to all latitudes by filling the empty cells with the average temperature value of their respective latitude.

GST reconstruction 1480 1530 1580 1630 1680 1730 1780 1830 1880 1930 1980 Here are the result of the GST history inversion. This animation shows the variations in time from 1480 to 1980.

Averaging scheme Because of the sparse spatial distribution of the boreholes, we used an averaging technique to compute the ground surface temperature history rather than a simple arithmetic average. The arithmetic average gives excessive weight to areas of high borehole density. In order to determine hemispheric average, different schemes have already been proposed. Mann et al. (2003) argued for an area-weighted average. Pollack and Smerdon (2004) have examined this method and another weighting scheme based on grid-cell occupancy.

Averaging scheme We reassess the continental northern and southern hemisphere average using a kilometric gridding instead of geographic aggregation. Thus, cells are of the same size and no area-weighting is required. Temperature data were averaged on 1000 km × 1000 km cells to avoid spatial aliasing and suppress redundancy. Some latitudes have a lot of filled cells; to avoid the distortion of the hemispheric representation, we gave the same weight to all latitudes by filling the empty cells with the average temperature value of their respective latitude.

Latitudinal average year polar temperate Latitude tropical temperate
Here is an latitudinal average on 5deg band to show the variations of GST according to the latitude. We would have obtained almost the same result using a 500km average. The average is not obtain with the same number of cell at each latitude. We may be confident of the result for the 40 to 55 deg band considering the number of cells used and their occupancy. Anyway, we have the same warming trend for the two last steps for each band of latitude. This warming is of .2 to .7 of amplitude. We can also notice the colder period between 40 and 55 around This may be related to the little ice age. Caution must be taken when interpreting this figure because the average change with the cell size and their position. temperate ΔT (K)

Hemispheric average Temperature change (K) Year Huang and
Pollack, 2000 (arithm. Avr.) 1 0.8 0.6 Mann et al., 1998 multiproxy 0.4 Temperature change (K) 0.2 The resulting averages GSTH from 558 northern hemisphere temperature profiles are shown in Figure 2. The latitudinal area-weighted averages are not significantly different and fall inside the error bar of the latitudinal kilometric averages whatever the cell size considered. This study -0.2 Stability range -0.4 1400 1500 1600 1700 1800 1900 2000 SH NH Year

Conclusions (1/4) The average GSTHs show an increase in the energy stored in the shallow subsurface, consistent with the expectations due to increased levels of greenhouse gases since the onset of the industrial revolution (Houghton et al., 2001). Average ground temperature increase is about 0.5°K during the last century for the south hemisphere and 0.3°K for the northern hemisphere; an arithmetic average shows more increase. The average northern hemisphere GSTH shows a marked increase in the energy stored in the shallow subsurface since about 1900, consistent with the expectations due to increased levels of greenhouse gases since the onset of the industrial revolution [Houghton et al., 2001]. Average ground temperature increase is about 0.5°K during this period. Labrador and Newfoundland show very little changes with respect to the long-term mean. This is consistent with at least the last 100 years of Environment Canada meteorological data collected in this area of Canada [Gullet and Skinner, 1992].

Conclusions (2/4) Areas in Central Canada show temporal variations consistent with previous analysis for data in this area (Beltrami and Mareschal, 1992; Beltrami et al., 2003). Labrador and Newfoundland show very little changes with respect to the long-term mean. This is consistent with at least the last 100 years of Environment Canada meteorological data collected in this area of Canada (Gullet and Skinner, 1992), which show a null trend for Newfoundland. The average northern hemisphere GSTH shows a marked increase in the energy stored in the shallow subsurface since about 1900, consistent with the expectations due to increased levels of greenhouse gases since the onset of the industrial revolution [Houghton et al., 2001]. Average ground temperature increase is about 0.5°K during this period. Labrador and Newfoundland show very little changes with respect to the long-term mean. This is consistent with at least the last 100 years of Environment Canada meteorological data collected in this area of Canada [Gullet and Skinner, 1992].

Conclusions (3/4) Regions in the Mid-West U.S.A. (Utah, for example) show little warming in recent years in agreement with meteorological data and with borehole temperature data from an independent data set not included in our analysis (Harris and Chapman, 2001). A colder period at the end of the 1800s is observed in central Europe; this is also supported by meteorological data (Zupancic, 1994). The average northern hemisphere GSTH shows a marked increase in the energy stored in the shallow subsurface since about 1900, consistent with the expectations due to increased levels of greenhouse gases since the onset of the industrial revolution [Houghton et al., 2001]. Average ground temperature increase is about 0.5°K during this period. Labrador and Newfoundland show very little changes with respect to the long-term mean. This is consistent with at least the last 100 years of Environment Canada meteorological data collected in this area of Canada [Gullet and Skinner, 1992].

Conclusions (4/4) The warming occurs sooner in the northern hemisphere than in the southern hemisphere where a cooling event took place until ~1800 according to the hemispheric average. Because of the sparse density of data in southern hemisphere, caution must be take when interpreting GSTH averages. Caution must be take when comparing average temperature history obtained from borehole inversion and proxy data since they are not representing the same region in most of the case. Furthermore, borehole data contain long-term history while proxy data contain short-term history. The average northern hemisphere GSTH shows a marked increase in the energy stored in the shallow subsurface since about 1900, consistent with the expectations due to increased levels of greenhouse gases since the onset of the industrial revolution [Houghton et al., 2001]. Average ground temperature increase is about 0.5°K during this period. Labrador and Newfoundland show very little changes with respect to the long-term mean. This is consistent with at least the last 100 years of Environment Canada meteorological data collected in this area of Canada [Gullet and Skinner, 1992].

Acknowledgements This research was funded by
the Canadian Foundation for Climate and Atmospheric Sciences (CFCAS) and the Natural Sciences and Engineering Research Council of Canada (NSERC). We are grateful of this support.

Evelise Bourlon Hugo Beltrami Environmental Earth Sciences Lab.

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