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    Map of the MAGS region of study (polar stereographic projection, standard parallels at 49° and 77°N). The names of some of the largest water bodies are indicated. In this figure, features smaller than about 10 km2 do not show because they were eliminated by filtering

  • View in gallery

    Location of measurement sites on Great Slave Lake during CAGES (based on Schertzer et al. 2003)

  • View in gallery

    Water temperature time series for (a) OD at 0.3- vs 5-m depth, (b) NW1 at 0.3 vs 2 m, (c) NW2 at 0.3 vs 2 m, and (d) IWI at 0.3 vs 2 m, during 1999. The heavy line corresponds to the 0.3-m data. The thin dashed line corresponds to the deeper (2 or 5 m) data

  • View in gallery

    (Continued)

  • View in gallery

    Comparison between AVHRR lake water temperature retrievals and 2-m buoy data at two buoy sites over Great Slave Lake: (a) southernmost site (HR); (b) at a site near the center of the lake (NW1). The dark fluctuating line is buoy data, the circles are AVHRR data, the inverted curve is the quadratic fit to the AVHRR data. In (b), the thick curve is the fit with day 167 discarded as an outlier, as described in the text

  • View in gallery

    Fitted water temperature curves plotted from the coefficients for the water bodies listed in TABLE 1; Tmax values for each curve are plotted as triangles: (a) for all 52 water bodies [Average date of tmax occurrence is 1 Aug (day 213).]; and (b) for only Great Bear Lake (I), Great Slave Lake (II), Lake Athabasca (III), La Martre Lake (IV), Lake Claire (V), and Lesser Slave Lake (VI)

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    Latitude effect on the evolution of Tw. Fitted curves for each 2° latitude band from 50° and 60°N were averaged

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The Evolution of AVHRR-Derived Water Temperatures over Lakes in the Mackenzie Basin and Hydrometeorological Applications

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  • 1 Climate Processes and Earth Observation Division, Climate Research Branch, Meteorological Service of Canada, Downsview, Ontario, Canada
  • | 2 Aquatic Ecosystems Impacts Research Branch, National Water Research Institute, Burlington, Ontario, Canada
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Abstract

The temperature evolution of water bodies is determined and compared over the Mackenzie River hydrological basin. The thermal IR observations used to determine the water temperatures were extracted from NOAA's Advanced Very High Resolution Radiometer (AVHRR) satellite data over the period from April 1999 to September 1999. The IR temperatures were calibrated and adjusted to account for the intervening atmosphere. For each day, 1-km-resolution temperature scenes were generated. From the temperature scenes, clear-sky temperature values were extracted for water bodies with areas larger than 100 km2. The temperature cycle over water bodies can be decomposed into a small positive slope from near 0°C until the water temperature reaches 4°C, followed by a quadratic trend that can be easily fitted. The quadratic curve fit parameters give information for cataloging and comparing each water body's seasonal temperature cycle. Data stratification confirms a strong latitudinal influence on the shape of the curves. Compared to Great Slave Lake, the duration of open water for Lake Athabasca is longer and begins about 16 days earlier; for Great Bear Lake, the cycle is shorter and begins about 45 days later. Fitted maximum temperatures are 15.5°C for Lake Athabasca, 13.7°C for Great Slave Lake, and 6.8°C for Great Bear Lake. The AVHRR-derived seasonal temperatures should be useful in estimating total lake evaporation because lakes with longer and warmer seasonal temperature cycles should tend to evaporate over longer time periods than those with shorter and cooler temperature cycles.

Corresponding author address: Normand Bussières, Climate Processes and Earth Observation Division, Climate Research Branch, Meteorological Service of Canada, 4905 Dufferin St., Downsview, ON M3H 5T4, Canada. Email: Normand.Bussieres@ec.gc.ca

Abstract

The temperature evolution of water bodies is determined and compared over the Mackenzie River hydrological basin. The thermal IR observations used to determine the water temperatures were extracted from NOAA's Advanced Very High Resolution Radiometer (AVHRR) satellite data over the period from April 1999 to September 1999. The IR temperatures were calibrated and adjusted to account for the intervening atmosphere. For each day, 1-km-resolution temperature scenes were generated. From the temperature scenes, clear-sky temperature values were extracted for water bodies with areas larger than 100 km2. The temperature cycle over water bodies can be decomposed into a small positive slope from near 0°C until the water temperature reaches 4°C, followed by a quadratic trend that can be easily fitted. The quadratic curve fit parameters give information for cataloging and comparing each water body's seasonal temperature cycle. Data stratification confirms a strong latitudinal influence on the shape of the curves. Compared to Great Slave Lake, the duration of open water for Lake Athabasca is longer and begins about 16 days earlier; for Great Bear Lake, the cycle is shorter and begins about 45 days later. Fitted maximum temperatures are 15.5°C for Lake Athabasca, 13.7°C for Great Slave Lake, and 6.8°C for Great Bear Lake. The AVHRR-derived seasonal temperatures should be useful in estimating total lake evaporation because lakes with longer and warmer seasonal temperature cycles should tend to evaporate over longer time periods than those with shorter and cooler temperature cycles.

Corresponding author address: Normand Bussières, Climate Processes and Earth Observation Division, Climate Research Branch, Meteorological Service of Canada, 4905 Dufferin St., Downsview, ON M3H 5T4, Canada. Email: Normand.Bussieres@ec.gc.ca

1. Introduction

Observations of lake water temperature are required for modeling heat and mass exchanges, as well as climatic impacts. For example, water temperature is a critical component in formulations of the vertical flux of heat above water surfaces (Laird and Kristovich 2002). Water temperatures are also part of the boundary conditions for earth–atmosphere models (Brasnett 1997). Water temperature observations are required for increased development of hydrometeorological applications. Because the quantitative aspects of the temperature cycle are not documented for most Canadian lakes, satellite observations are increasingly being used. Satellite infrared data are particularly useful in determining the spatial distribution of water body temperatures and their evolution during the year (Ullman et al. 1998). In this way, the satellite data have direct application in the important problem of scaling up data from lake buoys for application in hydrometeorological process models. Bussières et al. (2002) developed a method to observe and catalog the temperature cycle of Canadian water bodies. Therefore, our main study objectives are to extend this method to other regions and to apply earth–atmosphere and hydrometeorological modeling.

As indicated by Ginzburg et al. (1995), water temperature of ungauged water bodies can be simulated using one of three methods. In the first method, a reference water body for which the thermal regime is known serves as a guide to estimate the temperature of other water bodies that present similarities with the reference water body. In the second method, a lake model based on the heat budget is used, as in Goyette et al. (2000). In the third method, relationships between water temperature and the affecting factors are used. Application of thermal infrared techniques (Bussières et al. 2002) can serve, for example, to determine such relationships with affecting factors like latitude and lake morphology.

Within the framework of the Mackenzie Global Energy and Water Cycle Experiment (GEWEX) Study (MAGS) (Stewart et al. 1998), the heat exchange, evaporation, and thermal response of high-latitude lakes are being studied (e.g., Schertzer et al. 2002). For this experiment, National Oceanic and Atmospheric Administration (NOAA) Advanced Very High Resolution Radiometer (AVHRR) data were collected over the period April 1999 to September 1999. The region of study covered the Mackenzie River region in western Canada. One of the applications of this data collection is to determine each lake's water temperature cycle with AVHRR-infrared bands.

In this paper, time series of skin surface temperatures of boreal water bodies are extracted from AVHRR data under cloud-free conditions during the Canadian Enhanced GEWEX Study (CAGES) period. The water bodies studied are those sufficiently large to be observed clearly at AVHRR data resolution of 1 km2. It is assumed that for these water bodies, the seasonal temperature trend varies slowly enough that it can be captured even under the limited sampling rate, corresponding to cloud-free observations. The results of processing the AVHRR data, and calibrations with buoy data, are presented. The methodology of Bussières et al. (2002) is applied to determine the evolution of summer temperature for these water bodies. These trend curves are then analyzed on the basis of latitude and water body size in order to determine general parameters useful in the modeling of hydrometeorological processes. Effects of depth and annual variations are not examined due to the restricted database.

2. Observations and data processing

a. AVHRR data

For this study, NOAA-12 and NOAA-14 AVHRR satellite raw data were obtained from Environment Canada's high-resolution picture transmission (HRPT) site in Edmonton, Alberta, Canada. This AVHRR dataset was collected in the area of Fig. 1 for the period 1 April 1999 to 30 September 1999. Data from up to eight passes per day were processed, for a total of 849 passes. The passes occurred in the morning between 1000 and 1700 UTC, and in the afternoon between 2000 and 0200 UTC. In this region, western Canada (Fig. 1), at a longitude of 120°W, for example, local solar time is obtained by subtracting 8 h from UTC. The AVHRR satellite raw counts were converted to “percent albedo” (used here to detect clouds) and brightness temperatures, according to calibration procedures described in the NOAA Technical Memorandum, NESS 107 (Planet 1988). In NESS 107, the term percent albedo is used for the observational value of the “scaled radiance.” Scaled radiance is defined as π times the ratio of the observed top of the atmosphere in-band radiance to the extraterrestrial solar irradiance, for a given channel's wavelength band, at normal incidence at the top of the atmosphere at mean Earth–Sun distance. In accordance with the NESS 107 procedures, time-dependent gain and offset coefficients were obtained from NOAA and applied to the linear calibration of the visible channels from raw count to percent albedo. The thermal data were corrected for nonlinearity and converted to temperatures using the Planck function. Brown et al. (1993) reports that for AVHRR thermal channels in these conditions, an absolute radiometer calibration of ±0.44 K exists (square root of the sums of squares of contributing errors).

A 1-km polar stereographic projection was chosen for this work. A model of the satellite orbit around the earth serves to map the AVHRR data to the specified projection. Spatial resolution of AVHRR data at nadir is 1.1 km. In order to obtain the best spatial accuracy, remapping of each scene includes manual correction to the satellite's orbital parameters. The best passes corresponding to the smallest possible satellite zenith angle are chosen for the analysis.

AVHRR thermal IR channels 4 (10.3–11.3 μm) and 5 (11.5–12.5 μm) are used for the temperature analysis; channel 2 (0.725–1.10 μm) is also used to detect clouds. Multiple channel images for each scene are examined individually to determine the combination of thresholds in calibrated AVHRR channel-2 percent albedo and channel-4 calibrated brightness temperature that provide the best discrimination between land and clouds. In each scene, if a pixel value is higher than the selected percent albedo threshold or lower than the selected temperature threshold, the pixel is treated as cloudy. The effect of residual cloud contamination is discussed later in section 4. Over the study area, the average cloud cover estimated from all of the scenes from April 1999 to September 1999 is 59%.

The next processing step is to apply atmospheric adjustments to the brightness temperatures in order to obtain the water skin surface temperature (Ts) values. A split-window algorithm (Emery et al. 1994) yields an adjusted land/water surface temperature from channels 4 and 5 brightness temperatures. The algorithm is stated as
i1525-7541-4-4-660-e1
where T4 and T5 are the calibrated radiative temperatures from AVHRR channels 4 and 5, and the coefficients are a1 = −12.561 58, a2 = 1.049 03, a3 = 0.405 98, and a4 = 0.745 36.

The experimental AVHRR data for this study includes data for the spring period where the water bodies are still covered by ice. Equation (1) is not designed for ice, but Bussières et al. (2002) observed that a split-window equation for water allows to separate the ice regime from the open-water regime in AVHRR temperature time series.

b. Calibration of AVHRR data with buoy observations of lake water temperature

Measurements of Great Slave Lake water temperature were made from three meteorological buoys and also from five thermistor moorings (HR, OD, NW1, NW2, and IWI) over the lake (Fig. 2) along a transect from 60°53′N, 115°40′W to 61°39′N, 114°09′W (Schertzer et al. 2003). Observations from the meteorological buoys were conducted at ∼0.3 m from the surface and at a 2-m depth at all the thermistor moorings. Observations from the meteorological buoy were recorded at 10-min intervals, while thermistor mooring data were 20-min observations. Under wave conditions, the thermistor located on the meteorological buoy may traverse over a depth range of ±0.1 m. Alternatively, the thermistors located on the thermistor moorings are at fixed depths. A comparison between hourly temperature time series, observed at 0.3 and 5 m for OD and 0.3 and 2 m for NW1, NW2, and IWI, is shown in Figs. (3a–d). Although 2-m observations were available for HR, there were no 0.3-m temperatures available at this location in 1999. At the four sites with 0.3-m data, the correspondence between the 0.3- and 2-m (NW1, NW2, and IWI), or 5-m (OD) temperatures is in phase during the summer period. Departures are observed in the month of June in the period when ice is rapidly melting and when heating is confined to the near surface, especially under calm conditions (Schertzer et al. 2003). This is particularly evident at NW1 (Fig. 3b). Average differences between the temperature at 0.3- and 2-m (NW1, NEW, and IWI) and 5-m (OD) values for the four stations over the time series record is 0.45°C, which is excellent, considering that temperature observations were conducted with StowAway TidBiT loggers with an accuracy of ±0.2°C over the range −5° to +37°C (Schertzer et al. 2003). For sites with observations at 0.3- and 2-m depths (NW1, NW2, and IWI), the temperature observations show a high degree of correspondence with r = 0.97, and with an average vertical temperature difference of 0.40°C. This suggests that calibration of the current model with 2-m temperature observations introduces only a small temperature bias in the analysis of skin temperatures. Therefore, to provide a wider spatial coverage of the lake, we use the near-surface temperatures from the 2-m depth, which was operational throughout the entire 1999 experiment period. Furthermore, the Ts values computed from AVHRR data with Eq. (1) are proportional to the 2-m buoy data. Pooling data for NW1, NW2, IWI, and HR, the regression between Ts and Great Slave Lake buoy data, yields a water temperature (Tw) matched to 2-m buoy data:
Twb1b2Ts
where
b1b2
The linear correlation coefficient r2 = 0.88. The average bias (AVHRR Tw − 2-m buoy temperature) is 0.05°C, while the standard deviation of these differences is 1.7°C. Over the ocean, for which the algorithm was intended, Emery et al. (1994) report an rms value of 0.90°C for the difference between the temperatures computed with Eq. (1) and temperature data from ocean buoys. Here, the uncertainty in Tw can be estimated at ±1.9°C from a sum of the buoy temperature uncertainty (±0.2°C) and the observed standard deviation (1.7°C) over Great Slave Lake. The AVHRR radiometer calibration (±0.44°C) is treated as one of the components responsible for the uncertainty expressed by the standard deviation.

3. Spatial distribution of MAGS water bodies and method to determine their seasonal temperature time series

The Mackenzie River basin (1.8 × 106 km2) has a very large number of lakes (i.e., 30 000+) of various sizes (Rouse et al. 2002). There are several large lakes, for example, Great Bear Lake (net area: 30 764 km2), Great Slave Lake (net area: 27 048 km2), Lake Athabasca (net area: 7849 km2), La Marte Lake (net area: 1687 km2), and Lesser Slave Lake (net area: 1167 km2). The distribution (location and shape) of water bodies ≥10 km2 is illustrated in Fig. 1. The figure was generated by displaying and filtering the water class from the 1-km-resolution 1995 Canadian Centre for Remote Sensing (CCRS) land cover classification (Beaubien et al. 1997). Because the CCRS land cover data is in a projection different from the polar stereographic projection used in the current study, it had to be transformed. This was accomplished with an Earth transformation model (U.S. Geological Survey general cartographic transformation package), which provided the geographical coordinates of each pixel of the land cover map and its nearest location in the polar stereographic projection. Figure 1 shows that the largest concentration of water bodies is located in the eastern half of the Mackenzie basin.

In order to identify each water body separately, all of the groups of connected water class pixel classifications for the region of Fig. 1 are given a unique polygon identifier. The size of each polygon is determined by counting the number of pixels for the corresponding polygon identifier. This gives a total of 8900 distinct polygons covering 8% of the whole 1.8 × 106 km2 area. These polygons include all water bodies down to a single pixel size of 1 km2. Out of these polygons, only 113 are ≥100 km2, and only 799 are ≥10 km2. Over the Mackenzie basin, water bodies less than 10 km2 are much more frequent than the larger-sized ones. Rouse et al. (2002) suggest that the areal coverage of water bodies less than 10 km2 is dominant and that their overall contribution to evaporation is important.

The method that will be used here was described by Bussières et al. (2002) for boreal lakes in Manitoba, Saskatchewan, and Alberta. In order to avoid contamination of water pixels by land, all “water” pixels within 1 km from the shore are discarded. This is accomplished by creating, from the land cover data, a water–land mask corresponding to outline of the water bodies, and setting these outlines as nonwater pixels. The result of this “1-km filtering” procedure reduces the computational area over all of the water bodies, and eliminates completely many of the small ones. Because only the overall behavior of each water body is sought, the temperatures that are computed here are a spatial average of the pixels over the water body. In order to avoid data-sampling limitations with the smaller water bodies, a further limitation to water bodies of size ≥10 km2 is imposed. Although water bodies less than 10 km2 cannot be addressed here, this paper is useful to fill the gap between current studies of the smaller water bodies and those of larger lakes, such as Great Slave Lake.

A small number of polygons determined by this method can actually be islands within water bodies. The island polygons are not considered. Also, due to the limited data resolution, it is possible that some small water bodies are amalgamated into one polygon. Furthermore, some of the polygons were original parts of main water bodies due to the spatial filtering described above. These occurrences are noted below when they occur. There are also differences in the distributions of water polygon size and the distributions of actual water body sizes. Within the above-stated limitations, the term “water bodies” will be used here instead of “polygons” or “lakes.”

The time series are filtered to allow only observations for which 95% or more of the surface of the water body was classified as noncloudy. As suggested in Bussières et al. (2002), among the various curves (quadratic, higher-order polynomial, sinusoidal) that were tried to describe Tw as function of time, the quadratic was the simplest function that best matched the long-term variation of the time series data. A two-step process is used, similar to, but not as restrictive as, the method used by Ullman et al. (1998). In the first step, a least squares quadratic fit is applied to the time series. This allows us to detect some outliers, for example, colder temperature values that occur when clouds exist but are not detected in the earlier cloud discrimination and filtering steps. To filter out the outliers, the time series values differing by more than 7°C in absolute value from the fitted quadratic curve are rejected. The criteria takes into account that strong and rapid variations in water temperatures are possible and should not be discarded. In the second step, the quadratic fit is performed on the portion of the data beginning at the time where only above-zero temperatures are observed. The quadratic fit is defined as follows:
TAt2BtC,
where T is the water surface temperature fitted from the Tw observations, t is the number of days since 1 January of a given year, at 0000 UTC, and A, B, and C are empirical coefficients determined by least square fit [in Bussières et al. (2002) t was defined as the number of hours since 1 April].

The quadratic fit [Eq. (3)] describes the seasonal trend in a standard way so that various water bodies can be compared. It also provides a reference curve from which weather-related and daily variations can be subtracted, and the relative variations are intercompared, or compared with other types of data (Bussières et al. 2002). The fit is restricted to data from the open-water period only when the split-window coefficients of Eq. (1) are valid. Although observations made during most of the ice cover melting period are not used, the time of melt is deduced from extrapolation of the quadratic fit to the open-water data. For each water body, the following parameters can be computed from Eq. (3): the time (t0) at which the fitted temperature starts to rise above freezing, the time (t4) where temperature starts to rise above 4°C (i.e., temperature of maximum density for freshwater), and the time (tmax) at maximum fitted temperature (Tmax).

4. Characteristic data and temperature values of the curve fits over Great Slave Lake

Before the method is applied to the MAGS water bodies, data and curve fits at specific locations of Great Slave Lake are presented here to illustrate the method and characterize its uncertainties. Figures 4a and 4b show Great Slave Lake AVHRR Tw from AVHRR at the southernmost buoy site (HR; 60°53′08″N, 115°40′24″W) and at NW1, which is located at the center of the lake (NW1; 61°26′02″N, 114°46′35″W). The horizontal axis represents the days of year 1999. In the early part of the time series, the presence of ice cover is confirmed from images of the AVHRR visual bands. Around Julian day 140 for HR and day 150 at NW-1, the visual images indicate that the ice break-up process is underway at these two locations. Because ice and water coexist during this period, the application of the split-window algorithm [Eq. (1)] can only provide apparent values of Tw. The temperature estimates are probably biased toward lower values due the lower emissivity of ice compared to water. Actually, the first portion of the time series is characterized by apparent Tw values that are slightly below zero on average, with frequent temperature excursions in the 1°–2°C range. Overall, the first part of the time series is characterized by a slow and gradual increase in the apparent Tw values.

It is only after all of the ice has melted that the Tw values can increase rapidly as described by the data in Figs. 4a and 4b. With initial values near the temperatures of maximum water density (4°C), the second portion of the time series shows a rapid temperature rise, the temperatures peaking near mid-August (day 220 at HR, and day 227 at NW1). Some of the AVHRR values are much smaller than the buoy values. This is attributed to residual cloud contamination, which tends to make the AVHRR values appear lower. Some of the AVHRR values are higher than the buoy values, as, for example, near day 170 (mid-June) in Fig. 4b; because AVHRR senses the temperature from the skin surface, the rapid warming of the upper-water surface may not be transferred quickly to the 2-m level (e.g., Fig. 3c for site NW1 in June during the period of ice melt). The solid curves in Figs. 4a and 4b are quadratic fits to the Tw values, as determined over open water by the method in section 3. The resulting fit coefficients are as follows: for HR, they are A = −2.377 36 10−3°C day−2, B = 1.0477°C day−1, and C = 220.35°C; for NW1, they are A = −3.302 87 10−3°C day−2, B = 1.5012°C day−1, and C = −157.359°C.

Superposed on the seasonal variation are short-term fluctuations associated with the diurnal cycle and the passage of weather systems (e.g., Fig. 4). When the quadratic curve is subtracted from the original AVHRR data, the standard deviation of the resulting AVHRR signal plus observational noise is 1.7°C over HR and NW1. When the quadratic curve is subtracted from the buoy data, the corresponding standard deviations for the buoy data are 1.7°C over HR and 1.5°C over NW1, showing the consistency between near-shore and midlake applications of the technique.

The total uncertainty in temperatures computed from the AVHRR Tw temperature curve fits is ±2.2°C, based on the sum of Tw uncertainties (±1.9°C) and the standard estimate of error of the least squares fits (±0.3°C). Uncertainty about a given time (t4, e.g.) is obtained by substituting values of the temperature uncertainty range in Eq. (3) (T = 4°C ± 2.2°C at t4). Computed times and uncertainties at HR are then t0 = 138.7 ± 6 days and t4 = 149.8 ± 7 days. At NW1, t0 = 164.0 ± 6 days and t4 = 174.4 ± 7 days. An image from AVHRR visual data for day 160 shows that the Great Slave Lake surface area (excluding one of the northeastern arms of the lake, known as McLeod Bay, which is treated as a separate water body) is clear of ice on that day except for some patchy ice in the middle of the lake. A visual image for day 163 shows that the ice in the middle of Great Slave Lake has also disappeared. Bussières et al. (2002) had suggested that the t4 value is indicative of the time when a water body is completely free of ice, but here, the t4 values at NW1 appears late by 11 days. In the data for the NW1 time series, shown in Fig. 4b, the last two occurrences of a date when a value ≤0 are at days 152 and 167. The visual image on day 167 indicates about one-third of the lake covered by clouds. In this case, the cloud detection algorithm was not successful. In addition, the visual image for day 163 indicates no ice, and the average temperatures between days 152 and 167 is 1.5°C. Neglecting the value on day 167, a new fit is obtained, as shown by the thicker curve in Fig. 4b. With new fit coefficients of A = −2.706 98 10−3°C day−2, B = 1.2334°C day−1, and C = −127.722°C, the corresponding times for NW1 are t0 = 159.1 ± 6 days and t4 = 170.9 ± 7 days.

For Great Slave Lake as a whole, the fit coefficients are A = −2.629 76 10−3°C day−2, B = 1.1809°C day−1, and C = −118.926°C. This yields t0 = 152.5 ± 6 days and t4 = 163.9 ± 7 days. As indicated above, Great Slave Lake is free of ice on day 163. An analysis of passive microwave images indicates that this date could be day 161 ± 2 days (Schertzer et al. 2002). Although the t0 and t4 values for Great Slave Lake appear meaningful, the above uncertainty analysis shows that their accuracy is limited. This, and the example for NW1, suggest that questions of cloud filtering, accuracy of temperatures, and fitting function must be addressed to achieve better accuracy.

5. The seasonal trends

Table 1 summarizes, for 52 of the water bodies of area ≥100 km2, as well as for a few of the smaller ones, the coefficients of the fit curves and the parameters derived from Eq. (3). When applying to all the water bodies the technique stated in the previous section, estimated uncertainty is ±6 days on average for t0 and ±7 days for t4. The last three columns of Table 1 contain the actual water body net area (W; km2), the effective water body area (E; km2), and the latitude (decimal degrees) of each water body. The W values are from lake inventories (Demers 1975), and the E values are the number of pixels in the water polygon. As noted above, E is smaller than W due to the removal of edges with the 1-km filter technique described in the previous section. In certain cases, as for the water bodies named “MacKay_2263” and “MacKay_2078”, these are portions of Lake MacKay that were subdivided by the filtering technique. For these two portions of Lake MacKay, the values “E” are assigned in proportion of the respective number of pixels in each two polygons. As noted in the above section, Great Slave Lake is separated into the “Great Slave Lake” and “McLeod Bay” water bodies.

The curves for the water bodies in Table 1 are plotted in Fig. 5a. Because the input AVHRR data ranges from 1 April to 30 September, the portion beyond 30 September is not presented here. Table 1 and Fig. 5a show that there is substantial variation over the geographical area under study. The shortest temperature cycle in Fig. 5a corresponds to 30 764 km2 size Great Bear Lake at 66°N. Great Bear Lake is the deepest of all of the lakes plotted here. The longest cycle corresponds to 22 km2 sized Watta Lake at 62°N. The average date for tmax is 1 August (day 213). The region previously studied in Bussières et al. (2002) was centered farther south (around 55°N) than the current study; and for that region, the average date for tmax is 25 July (day 206), which is not such a large difference, considering also the differences in location, data year (1994), and lake size distribution. The standard deviation of t4 values is 16 days where for the tmax values it is only 7 days. This interesting phenomena is clearly visible in Fig. 5a where the curves are spread by many weeks at the beginning of the season but tend to converge at the end of the period. Values of Tmax are also plotted against time tmax as triangles in Fig. 5a. This shows that Tmax is inversely related to tmax.

According to Ragotzkie (1978), the water temperature cycle of a lake is a function first of the climate and second of the morphology of the water body. Water transparency can also influence the temperature cycle by affecting the mixing depth (Fee et al. 1996). Over the study area, there are variations in water body shape, bathymetry, chemistry, and climatological conditions. Consequently, each water body may undergo a distinctive surface temperature evolution, as shown in Fig. 5a. It is then interesting to determine the influence of affecting factors, as suggested in Ginzburg et al. (1995). The extent to which the temperature cycles can be grouped in categories could be useful in understanding the behavior of the Mackenzie basin water bodies and for establishing modeling practices for the study area.

Results are similar to those found in (Bussières et al. 2002). The linear correlation coefficients between the latitudes and the following parameters from Table 1 are with time t0 (r2 = 0.46) and with time t4 (r2 = 0.44). Linear correlation between latitude and with maximum temperature Tmax is (r2 = 0.31), which is less than observed in the previous work. Correlation between water body area and t0, t4, and Tmax are less than for the above values for latitude.

Even if the correlation coefficients are low and, therefore, not very useful for quantitative work, consistent relationships appear between t0, t4, tmax, Tmax, and latitude. These relationships are particularly clear for the larger lakes, as shown in Fig. 5b, that is, for Great Bear Lake (I), Great Slave Lake (II), Lake Athabasca (III), La Martre Lake (IV), Lake Claire (V), and Lesser Slave Lake (VI). The length and amplitude of the temperature cycle increases as the size of the water body decreases. On the other hand, the similarity of the curves between Lake Athabasca (W = 7849 km2, latitude = 59.11°N) and La Martre Lake (W = 1687 km2, latitude = 63.32°N) in Fig. 5b suggest that simple relationships do not exist between the above parameters.

Average depths (that is, volume/area) are known for four water bodies in Fig 5b: about 30 m for Great Slave Lake (II), 26 m for Lake Athabasca (III), 1.2 m for Lake Claire (V), and 12 m for Lesser Slave Lake (VI). Great Bear Lake is also though of as being the deepest of all. The length and amplitude of the temperature cycle appear inversely related to depth, but it is probably not a simple relationship. For example, this does not work when comparing the temperature curves and mean depth for Lake Claire and Lesser Slave Lakes.

Figure 6 shows a curve that was generated for each 2° latitude band by taking the average of the fitted curves for all of the water bodies within that band. According to Fig. 6, the southernmost water bodies have longer and warmer cycles than northernmost lakes. The same figure also shows that times t0 and tmax occur later with increasing latitude; Tmax decreases with latitude.

As noted in Bussières et al. (2002), there is insufficient depth and lake bathymetry information to generate statistically meaningful relationships with the parameters from Table 1. Using the parameters in Table 1, multilinear regression would appear useful, as in Gao and Stefan (1999). However, in the absence of lake depth, it seems better again for now to describe directly each individual lake's temperature evolution directly by the individual coefficients A, B, and C of Eq. (3).

6. Hydrometeorological applications over the Mackenzie basin lakes

An important goal of MAGS is to understand the circulation, storage, and distribution of water and energy in the Canadian northern climate system. During CAGES, research on the lakes component has focussed on quantifying the thermal regime and heat storage, as well as heat and mass transfers across the air–water interface (e.g., Schertzer et al. 2003; Rouse et al. 2003) Intensive measurements and modeling has been conducted on only a small sample of the lakes illustrated in Fig. 1. Remote sensing techniques, such as those described in this paper, are crucial for extension of the lakes research over expansive basins, such as the Mackenzie basin.

This paper describes a methodology to derive surface temperature for lakes based on AVHRR satellite data. Water surface temperature is one of the fundamental physical limnological variables. For hydrometeorological research over lakes, it enters into computations to determine ambient meteorological conditions, such as saturation vapor pressure and atmospheric stability (e.g., Schertzer et al. 2003). The surface temperature is also a critical variable for determining energy flux emitted from the water surface and in turbulent exchange processes (e.g., Rouse et al. 2003; Blanken et al. 2000). For large lakes, in particular, the water temperature can exert a moderating influence on the regional scale.

One example of potential hydrometeorological application of the present methodology is for estimation of evaporation over the extensive Mackenzie basin lakes. Within the Mackenzie basin GEWEX investigation, Rouse et al. (2002) derived a conceptual model of landscape evaporation for lakes categorized as small, medium, and large. The model suggested that the contribution to evaporation from the numerous small lakes is considerable and collectively of the same order of magnitude compared to evaporation from the few very large lakes. It was suggested that to scale results over the basin, information on the lake geometry (i.e., surface area, depth, volume), and temperature were critical in order to estimate total lake evaporation over the Mackenzie basin. Figure 1 shows that the AVHRR data are useful for determining surface areas of lakes ≥10 km2. This, and information from the higher-resolution Canadian National Topographic Database, indicate that water bodies, including those smaller than 10 km2, are concentrated in the region to the east of a line that goes from Great Bear Lake to Lake Athabasca.

The surface of Lake Athabasca is about 3.4 times smaller than Great Slave Lake. Table 1 and Fig. 5b show that the duration of open water for Lake Athabasca is longer and begins about 16 days earlier than for Great Slave Lake. For Lake Athabasca, fitted Tmax (15.5°C) is warmer than for Great Slave Lake by about 2°C. Comparatively, Great Bear Lake is about 1.1 times larger than Great Slave Lake. The duration of open water for Great Bear Lake is shorter and begins about 45 days later than for Great Slave Lake. Of all of the lakes reported in Table 1, Great Bear Lake is the latest to reach the 4°C threshold, and has the lowest fitted Tmax (6.8°C). When the mass transfer approach is used to compute lake evaporation, the computed evaporation is proportional to wind speed and to the difference in saturation vapor pressures at water and air temperatures (Shertzer et al. 2003). Evaporation computations are beyond the scope of this paper, but we can assume that over the length of the open-water season, the sum of the differences in saturation vapor pressure could be higher for lakes with the highest Tmax and the longest open water duration. We suggest here that because lakes with longer and warmer seasonal temperature cycles should tend to evaporate over longer time periods than those with shorter and cooler temperature cycles, our AVHRR-derived seasonal temperatures should be useful in estimating total lake evaporation. For this purpose, future research will be required to relate the seasonal temperature cycle information, like that reported in Table 1, with annual lake heat content and heat exchanges for lakes within different size classifications.

7. Conclusions

Even if the presence of clouds limits the sample size, it has been shown that there are enough clear-sky AVHRR observations over the Mackenzie basin to build up useful time series of lake water temperatures. The temperature cycle over boreal lakes, as determined from AVHRR data, can be decomposed into a small positive slope for the spring ice break-up period, followed by a quadratic curve for the open-water temperature variations. A quadratic is the simplest function that can describe well the open-water seasonal temperature variation.

The quadratic function fitted to the time series yields characteristic dates t0 and t4 when the water reaches 0° and 4°C, and the date tmax of the maximum temperature value of the warm season. The uncertainties in fitted temperatures (±2.2°C) serve to estimate the time uncertainties to ±6 days for t0 and ±7 days for t4. The method was designed to determine and compare the seasonal temperature evolution of water body temperatures from AVHRR over a region. If the objective was the study of lake ice breakup, a higher accuracy would be necessary. Comparisons of lake ice conditions and air temperature records for Canadian lakes (Skinner 1993) indicate that a 3°C change in mean May air temperature corresponds to an approximate 8-day change in the ice breakup date. Reduction of uncertainty in our proposed method requires improvements in cloud filtering, reduction in uncertainty of water temperature estimates, and improving the selection and the fit of a function to the Tw values.

The quadratic fit coefficients and associated time and temperature parameters vary from water body to water body. Latitude is a significant parameter, while the water body area is less significant. Bathymetric data were not available for the majority of the water bodies in this study. In the absence of all of the information required to simulate the water temperatures from affecting factors, the empirical fit coefficients that describe each water body as provided in this paper must be used directly. For most of the Canadian lakes, characteristics other than their size are unknown.

Water surface temperature is an important variable in computation of hydrometeorological processes, such as heat and mass exchanges of lakes. Within the CAGES lake analyses, heat and mass exchanges have been computed based on high-frequency data from eddy correlation and also from hourly and daily scales (Schertzer et al. 2003; Rouse et al. 2003; Blanken and Rouse 2003). The shape, length, and amplitude of the temperature cycle for open water, as determined from AVHRR, should be useful in estimating corresponding differences in total lake evaporation. The results presented in this paper, do not include daily variations of water temperature. However, it appears possible to build a model time series by combining the seasonal trends from AVHRR data and the variations from weather station data, as suggested in Bussières et al. (2002). Current work is under way to evaluate this concept. In applications over the large number of lakes within the Mackenzie basin, longer time averages (e.g., weekly mean temperatures) may be the most practical, considering that there is little ancillary information, such as lake geometry, over-lake meteorology, etc. for high-frequency heat and mass exchange evaluations.

We have examined only observations over a season. Observations of year-to-year variations in the seasonal water temperature trends of water bodies would be of interest to the modeling of climate change. Studying year-to-year variations requires a continuous infrared dataset at sufficient resolution, proper calibration of the data to account for drift in sensor performance, accurate ground georeferencing, and improvement in accuracy, as indicated above. Although we have illustrated in principle how the basic work can be done, AVHRR data, the Moderate Resolution Imaging Spectroradiometer (MODIS) sensor data from satellites like Terra and Aqua can probably meet most of these requirements.

This paper has demonstrated that the current approach for computing surface water temperature over a large lake, such as Great Slave Lake, can provide information on the main characteristics of the seasonal temperature cycle. The examples shown in Fig. 5 show that the methodology can provide useful information in estimating the time of ice-free conditions, the beginning of lake stratification when the lake temperature reaches 4°C, and providing data to generate curves to describe the seasonal temperature trend. Comparisons between AVHRR-derived temperature and temperature at 2-m depth show consistent results over five lake sites along a midlake cross section. This is particularly encouraging because the methodology was successful over lake sites varying between 15- and 103-m depths, which can have significant differences in the seasonal temperature distribution and magnitude of temperature. On average, the Ts values computed from AVHRR are proportional with the 2-m lake temperatures with average bias between AVHRR and observed data at 0.05°C with explained variations of r2 = 0.88.

Acknowledgments

Thanks to Ron Goodson of the MSC Branch, Prairie and Northern region, and Environment Canada for access to Edmonton station's AVHRR data. Thanks also to Walter Skinner of MSC and the Journal of Hydrometeorology reviewers for very useful comments and suggestions.

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Fig. 1.
Fig. 1.

Map of the MAGS region of study (polar stereographic projection, standard parallels at 49° and 77°N). The names of some of the largest water bodies are indicated. In this figure, features smaller than about 10 km2 do not show because they were eliminated by filtering

Citation: Journal of Hydrometeorology 4, 4; 10.1175/1525-7541(2003)004<0660:TEOAWT>2.0.CO;2

Fig. 2.
Fig. 2.

Location of measurement sites on Great Slave Lake during CAGES (based on Schertzer et al. 2003)

Citation: Journal of Hydrometeorology 4, 4; 10.1175/1525-7541(2003)004<0660:TEOAWT>2.0.CO;2

Fig. 3.
Fig. 3.

Water temperature time series for (a) OD at 0.3- vs 5-m depth, (b) NW1 at 0.3 vs 2 m, (c) NW2 at 0.3 vs 2 m, and (d) IWI at 0.3 vs 2 m, during 1999. The heavy line corresponds to the 0.3-m data. The thin dashed line corresponds to the deeper (2 or 5 m) data

Citation: Journal of Hydrometeorology 4, 4; 10.1175/1525-7541(2003)004<0660:TEOAWT>2.0.CO;2

Fig. 4.
Fig. 4.

Comparison between AVHRR lake water temperature retrievals and 2-m buoy data at two buoy sites over Great Slave Lake: (a) southernmost site (HR); (b) at a site near the center of the lake (NW1). The dark fluctuating line is buoy data, the circles are AVHRR data, the inverted curve is the quadratic fit to the AVHRR data. In (b), the thick curve is the fit with day 167 discarded as an outlier, as described in the text

Citation: Journal of Hydrometeorology 4, 4; 10.1175/1525-7541(2003)004<0660:TEOAWT>2.0.CO;2

Fig. 5.
Fig. 5.

Fitted water temperature curves plotted from the coefficients for the water bodies listed in TABLE 1; Tmax values for each curve are plotted as triangles: (a) for all 52 water bodies [Average date of tmax occurrence is 1 Aug (day 213).]; and (b) for only Great Bear Lake (I), Great Slave Lake (II), Lake Athabasca (III), La Martre Lake (IV), Lake Claire (V), and Lesser Slave Lake (VI)

Citation: Journal of Hydrometeorology 4, 4; 10.1175/1525-7541(2003)004<0660:TEOAWT>2.0.CO;2

Fig. 6.
Fig. 6.

Latitude effect on the evolution of Tw. Fitted curves for each 2° latitude band from 50° and 60°N were averaged

Citation: Journal of Hydrometeorology 4, 4; 10.1175/1525-7541(2003)004<0660:TEOAWT>2.0.CO;2

Table 1.

Coefficients of water temperature time series during the 1999 ice-free season for various water bodies

Table 1.
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