Multi-sensor analysis of water storage variations of the Caspian Sea

Transcription

1 GEOPHYSICAL RESEARCH LETTERS, VOL. 34, L16401, doi: /2007gl030733, 2007 Multi-sensor analysis of water storage variations of the Caspian Sea Sean Swenson 1 and John Wahr 2 Received 18 May 2007; revised 18 June 2007; accepted 20 July 2007; published 17 August [1] We perform a multi-sensor analysis of water storage and surface height variations of the Caspian Sea, from mid through Data from three satellite missions (GRACE, Jason-1, and Aqua) are used to examine the relationship between changes in spatially averaged sea surface height (SSH) and water storage in and around the Caspian Sea. Two composite time series are constructed to represent the mass change signal, the first by removing a model of nearby hydrological signals from the GRACE time series, and the second by subtracting a MODIS SSTbased estimate of thermal expansion from the Jason-1 time series. The composite time series agree well (rms difference = 5.2 cm), and a positive trend is seen in both the GRACE (4.5 ± 0.7 cm/) and Jason (3.2 ± 0.3 cm/) composite time series. This analysis provides an indirect means of validating these data at regional spatial and monthly temporal scales. Citation: Swenson, S., and J. Wahr (2007), Multi-sensor analysis of water storage variations of the Caspian Sea, Geophys. Res. Lett., 34, L16401, doi: / 2007GL Introduction [2] Validation of remotely sensed data products typically involves comparisons with in situ measurements. For example, the accuracy of Jason-1 altimetric SSH s has been assessed using tide gages [Woodworth et al., 2004] and temperature and salinity data along ship tracks [Arnault et al., 2004]; SST s derived from a number of satellites have been compared to temperature sensors on ships [Barton and Pearce, 2006] and buoys [Emery et al., 2001]; terrestrial water storage from GRACE has been verified against soil moisture and well level observations [Swenson et al., 2006]. In situ observations often represent only a small subset of the total area sampled by remote instruments, which for many satellite missions is global. In addition, validation experiments take place during a finite period of time, so while the results may be valid for a particular location and time, their applicability to other regions and time periods is unknown. [3] Indirect verification is possible when multiple satellites independently measure aspects of the same variable. For example, Chambers et al. [2004] estimated seasonal variations of global mean sea level from GRACE and a combination of Topex/Poseidon and Jason-1 data, and found good agreement after correcting for steric effects in the Jason-1 data, thus providing a comparative assessment 1 Advanced Study Program, National Center for Atmospheric Research, Boulder, Colorado, USA. 2 Department of Physics and Cooperative Institute for Research in Environmental Sciences, University of Colorado, Boulder, Colorado, USA. Copight 2007 by the American Geophysical Union /07/2007GL of the quality of the GRACE and Jason-1 datasets at the global scale. At the regional scale, Fenoglio-Marc et al. [2006] estimated mass change in the Mediterranean Sea using GRACE data [see also Garcia et al., 2006]. Their estimate of the mean annual cycle agreed with a stericcorrected altimetric estimate to within 7 mm in amplitude and 27 days in phase. We extend this approach here and examine the much smaller region of the Caspian Sea. Our study differs from that of Fenoglio-Marc et al. [2006] by 1) the use of Release-4 GRACE data, 2) the application of the Swenson and Wahr [2006] correlated-error filter, 3) steric corrections based on satellite-derived sea surface temperature data rather than an ocean circulation model, and 4) a different land surface model to correct for hydrological leakage. [4] This study uses satellite data from three missions: the Gravity Recovery and Climate Mission (GRACE) [Tapley et al., 2004], the Jason-1 Altimeter [Menard et al., 2003], and the Moderate Resolution Imaging Spectroradiometer (MODIS) [Esaias et al., 1998], aboard the Aqua satellite. By combining and comparing these independent datasets, one can use their consistency as a validation measure. The data products from these missions measure different, but overlapping, aspects of the water budget. GRACE senses changes in the Earth s gravity field, from which surface mass anomalies can be inferred. At the monthly timescale, these mass anomalies are dominated by the redistribution of water [Wahr et al., 1998]. Jason-1 measures changes in SSH, which may be caused by changes in mass and changes in density due to temperature and salinity variations. MODIS surface skin temperatures are used to estimate the near-surface bulk temperatures at depths of about 1 meter [Esaias et al., 1998]. Because the measurement techniques are distinct, the potential for common errors is limited. [5] We focus on water storage variations in the Caspian Sea to indirectly validate the output of these satellite datasets at regional spatial and monthly time scales. The Caspian Sea is an attractive target because it has large seasonal cycles of mass, height, and temperature. It also has an areal extent (436,000 km 2 ) that is large enough to be sensed by GRACE. 2. Data and Methods 2.1. GRACE Total Water Storage [6] The GRACE satellite mission, sponsored by NASA and its German counterpart DLR, has been collecting data since mid The nominal data products are monthly Earth gravity fields [Tapley et al., 2004]. These can be used to make global estimates of vertically integrated terrestrial water storage (TWS) with a spatial resolution of a few hundred km and greater, with higher accuracy at larger spatial scales [Wahr et al., 2004]. L of5

2 Figure 1. Map of the Caspian Sea. Contours are values of the GRACE averaging kernel. [7] We use Release-4 data produced by the Center for Space Research at the University of Texas. Each monthly GRACE gravity field consists of a set of spherical harmonic (Stokes) coefficients. Degree 1 terms are not part of the solution, so we estimate them from a combined landsurface/ocean model. After removal of the temporal mean, each monthly GRACE field is filtered using the method of Swenson and Wahr [2006], and converted to mass in units of equivalent water thickness. [8] To assess the uncertainty in the filtered GRACE coefficients, the method of Wahr et al. [2004] is used. In brief, a high-pass filter that removes frequencies of once and twice per year is applied to the time series of each coefficient. The temporal RMS of the residual is used as an estimate of the upper bound on the random component of the error. This estimate is conservative, because intra-annual variations in the signal will be interpreted as error. The 1-s error estimates in the spatially averaged GRACE time series are then calculated from the estimates of uncertainty in the individual Stokes coefficients [Swenson and Wahr, 2002]. [9] Because of a lack of in situ observational networks of total water storage with spatial resolution comparable to that of GRACE, there are currently few opportunities to validate GRACE. In a validation study focused on Illinois, RMS differences between GFZ-Potsdam Release-3 GRACE TWS estimates and in situ observations were 2 cm for a region of 280,000 km 2 [Swenson et al., 2006] Spatially Averaged Time Series [10] GRACE Stokes coefficients can be used to estimate water storage variations averaged over regions with a minimum area of order 200,000 km 2. Because errors in the GRACE coefficients increase with spherical harmonic degree, averages are typically computed using a set of nonuniform weights [Swenson and Wahr, 2002]. In this study, we construct an averaging kernel for the Caspian Sea by convolving a 300 km halfwidth Gaussian function with the Caspian Sea mask (defined as 1 at points inside the Caspian Sea and 0 outside). Figure 1 shows the contours of the resulting spatial averaging kernel. The monthly, spatially averaged GRACE TWS anomalies are shown in the first panel of Figure 2. The circles indicate monthly values, and the smooth line is the result of applying a low-pass filter. The time series is largely seasonal, with an amplitude of about 60 mm and a maximum in late spring. The RMS error in the monthly values is 23.4 mm. Also shown is the bestfitting linear trend, of 18.9 ± 2.7 mm. A large drop in storage can be seen in late 2006, returning the lake mass to almost the level of The trend for mid-2002 through the end of 2005 is 36.5 ± 4.0 mm Leakage From the Surrounding Land [11] Because spatial averaging is required to produce a reasonable signal-to-noise ratio from the GRACE data, the averaging kernel shown in Figure 1 is a smoothed version of the Caspian Sea mask. The mass results are thus contaminated by signals outside the Caspian Sea. To reduce this leakage, an independent estimate of the surrounding mass variability is needed. We use simulations of TWS from a land surface model (LSM) produced by NASA s Global Land Data Assimilation System [Rodell et al., 2004]. These data are processed like the GRACE data: gridded data are converted to the spectral domain, truncated to degree 60, and filtered and spatially averaged to create a time series of monthly TWS anomalies. 2of5

3 Figure 2. GRACE total water storage (TWS) variations (first panel). Circles are monthly averaged TWS anomalies, solid lines are low-pass filtered time series and best-fitting linear trend. Mass leakage estimated from land surface model (second panel). Jason-1 time series (third panel); left y-axis represents GRACE-like values, right y-axis represents original sea surface heights. MODIS time series (fourth panel); left y-axis represents GRACE-like height variations, right y-axis represents original sea surface temperature anomalies. X-axis is the date. [12] This time series is shown in the second panel of Figure 2. It is dominantly seasonal with an amplitude of about 20 mm. The LSM time series peaks in early spring, about 2 months earlier than that for GRACE, the difference reflecting the transport time of streamflow from the surrounding watershed into the Caspian Sea. The best-fitting linear trend, 1.65 mm, explains <10% of the trend seen in GRACE, indicating that the Caspian Sea itself is the primary source of the GRACE trend, and not leakage from neighboring regions Jason-1 Sea Surface Height [13] Although the primary focus of the Jason-1 altimeter is to map oceanic SSH, it also detects water level changes in lakes and inland seas [Cazenave et al., 1997; Birkett, 1998]. The U.S. Department of Agriculture s Foreign Agricultural Service uses Jason-1 data to routinely monitor height variations of approximately 100 large lake and reservoirs globally. Time series of altimetric lake level variations from the USDA Reservoir Database may be obtained from: [14] Validation of satellite altimeter data over inland water bodies is typically performed by comparing altimetric time series and in situ stage measurements. The accuracy of elevation variations derived from the Topex/Poseidon mission has been estimated at 3 4 cm RMS for the largest lakes [Birkett, 1995]. In many places, however, stage observations are not available. [15] To construct altimetric values that are commensurate with the GRACE water storage time series, the Jason-1 data are temporally averaged to monthly values. These values cannot be directly compared to the GRACE results, because our processing reduces the GRACE Caspian Sea signal. To determine that reduction, we apply the GRACE filtering and spatial averaging procedures to gravity data that simulate the contribution from a uniform 1 mm (non-steric) rise of the Caspian Sea. We obtain 0.37 mm. We conclude that the GRACE processing reduces the true Caspian Sea signal by a factor of 0.37, and so we multiply the Jason-1 time series by that factor to compare with GRACE. [16] The original Jason-1 values are shown in the third panel of Figure 2 as a thick black line. The right-hand axis, which denotes values before multiplying by 0.37, shows that the SSH seasonal cycle in the Caspian Sea has an amplitude of about 30 cm. The GRACE-like time series, shown by the circles and smooth line and represented by the numbers on the left-hand axis, has a larger amplitude than GRACE, about 75 mm. The phase of the Jason-1 time series lags GRACE by 1 2 months, peaking in mid-summer. The best-fitting linear trend has a smaller value than GRACE, 12.1 ± 0.8 mm. Between mid-2002 and the end of 2005 the trend is over twice as large, 27.9 ± 1.2 mm Aqua/MODIS Sea Surface Temperature [17] The Aqua/MODIS instrument measures infrared radiation upwelling from the Earth s surface [Esaias et al., 1998]. MODIS senses 36 spectral bands, with global coverage every 1 to 2 days. The IR radiances are used to estimate the skin (upper 1 mm or less) SST, which is then related to subsurface, or bulk, SST in the mixed layer. Here we use Level-3 data from NASA s Ocean Biology Processing Group, binned to monthly temporal and 9 km spatial resolution, available from The gridded values are spatially averaged over the Caspian Sea. [18] Validation of satellite SST typically employs data from in situ, shipborne radiometers to calibrate the radiances measured by the satellite to those at the surface. Additionally, empirical relationships between skin and bulk temperatures must be developed, and these may vary in time 3of5

4 Figure 3. (top) GRACE water storage time series, corrected for leakage. (middle) Jason-1 time series, corrected for thermal expansion. (bottom) Comparison of the two time series. Both time series have been rescaled to account for amplitude damping of GRACE averaging kernel. Y-axis is mm water height; x-axis is the date. Both time series have been rescaled to account for filtering effects and truncation from the GRACE spatial averaging process. and space [Donlon et al., 2002]. Oesch et al. [2005] compared MODIS SSTs to in situ temperature measurements in a number of lakes in Europe and found biases of <2 K Converting Temperature Anomalies to Water Height [19] Changes in water temperature are accompanied by changes in volume. Assuming the thermal expansion coefficient, a, is independent of depth in the mixed layer, changes in SSH due to thermal expansion are linearly related to vertically integrated changes in bulk SST [Jayne et al., 2003]. The thickness of the near surface mixed layer, where most temperature fluctuations take place, is estimated from temperature profiles obtained from the World Ocean Database 2005 [Boyer et al., 2006]. The lower boundary of the mixed layer is identified by a strong temperature gradient [Pond and Pickard, 1991]. In a plot of temperature as a function of depth compiled from 40 profiles measured in the Caspian Sea (not shown), a decrease in temperature from 25 to 7 occurs at depths between 25 and 30 m. We use the average depth over this range, 28.1 m, as an estimate of the mixed layer depth. Multiplying this thickness by a = K 1 gives a conversion factor of mm that can be used to estimate the change in SSH from the change in SST. Using this factor, an uncertainty of 2 K will lead to an uncertainty of 16.9 mm in SSH. [20] The original SST time series is shown in the fourth panel of Figure 2 as a thick black line. The y-axis at the right of this plot shows that temperature variations in the Caspian Sea vary by about 20 annually. After converting the SST anomalies to height variations and multiplying by the 0.37 factor to account for the effects of GRACE processing, the time series has an amplitude of approximately 20 mm, and peaks in late summer, 2 4 weeks later than the SSH time series. The linear trend is 0.5 ± 0.7 mm. 3. Results [21] From the four datasets shown in Figure 2, two composite time series are constructed representing the mass change SSH signal in the Caspian Sea. The first (GRACE*) is computed by removing the land surface model estimate of the effects of nearby hydrological signals from the GRACE TWS time series. The GRACE* values have been divided by the amplitude damping factor 0.37, so that the values now represent the true non-steric SSH variability in the Caspian Sea. The second time series (Jason*) uses the MODIS SST-based estimate to remove thermal expansion effects from the Jason-1 time series, and the GRACE damping factor is no longer applied. Figure 3 (top) shows the GRACE* time series, Figure 3 (middle) shows the Jason* time series, and Figure 3 (bottom) compares the two. Each panel also shows the best-fitting linear trend, as well as the low-pass filtered time series, as solid lines. [22] While still seasonal in nature, both time series are less purely sinusoidal than the non-composite GRACE and Jason-1 results, showing a more gradual increase from the autumn to mid-summer, followed by a rapid decrease from mid-summer to autumn. The removal of the leakage signal reduces the amplitude of the GRACE time series by about 20%, and delays the phase by about one month. The removal of the SST values reduces the amplitude of the Jason-1 time series and advances its phase by 1 2 weeks. The resulting phases of the GRACE* and Jason* time series agree to within 1 2 weeks. The GRACE* and Jason* trends also agree well, with values of 45.3 ± 7.3 mm and 32.2 ± 2.8 mm, respectively. The RMS difference between 4of5

5 the two time series is 52.4 mm, and is 40.5 mm after low-pass filtering to remove frequencies greater than twice per year. [23] Using the method of Wahr et al. [2004], we estimate the uncertainty in the monthly GRACE fields to be 23.4 mm, which becomes 63.2 mm when rescaled. The fact that this is larger than the RMS difference implies that this method is conservative, and the assumption that all high frequency variations are noise is overly pessimistic. 4. Summary [24] We have analyzed data from three satellite missions, each sensing a different part of the water cycle. After applying equivalent processing techniques, the resulting composite time series agree well, providing a measure of uncertainty at regional scales. Verification at this spatial scale is currently lacking due to the absence of broad networks of in situ data, and this study therefore complements localized validation studies. [25] In addition to providing a means of assessing the quality of the datasets, multi-sensor analyses enable the separation of signals from different physical processes, e.g. isolating the relative contributions of mass and thermal expansion in altimetric SSH. In some cases this may aid in discriminating between natural variability and humaninduced change. For example, the datasets analyzed here indicate that the increase in the Caspian Sea water levels is not due to increased heat storage, but to increased water mass. Furthermore, the GRACE TWS time series for the entire watershed (not shown) shows a similar positive trend, implying that the basin is responding to increased net precipitation. If the trend in the surrounding watershed were found to be insignificant, i.e. the Caspian Sea was responding independently of the watershed, then this could indicate possible anthropogenic influences such as dam regulation or river diversion. [26] Acknowledgments. 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