• Adler, R. F., , G. J. Huffman, , D. T. Bolvin, , S. Curtis, , and E. J. Nelkin, 2000: Tropical rainfall distributions determined using TRMM combined with other satellite and rain gauge information. J. Appl. Meteor., 39, 20072023.

    • Search Google Scholar
    • Export Citation
  • Alsdorf, D., , C. Birkett, , T. Dunne, , J. Melack, , and L. Hess, 2001: Water level changes in a large Amazon lake measured with spaceborne radar interferometry and altimetry. Geophys. Res. Lett., 28, 26712674.

    • Search Google Scholar
    • Export Citation
  • Anyah, R. O., , F. H. M. Semazzi, , and L. Xie, 2006: Simulated physical mechanisms associated with climate variability over Lake Victoria basin in East Africa. Mon. Wea. Rev., 134, 35883609.

    • Search Google Scholar
    • Export Citation
  • Anyamba, A., , and J. R. Eastman, 1996: Interannual variability of NDVI Africa and its relation to El Niño–Southern Oscillation. Int. J. Remote Sens., 1, 25332548.

    • Search Google Scholar
    • Export Citation
  • Ashok, K., , Z. Guan, , and T. Yamagata, 2001: Impact of the Indian Ocean dipole on the relationship between the Indian monsoon rainfall and ENSO. Geophys. Res. Lett., 28, 44994502.

    • Search Google Scholar
    • Export Citation
  • Avakyan, A. B., , and V. B. Iakovleva, 1998: Status of global reservoirs: The position in the late twentieth century. Lakes Reservoirs: Res. Manage., 3, 4552.

    • Search Google Scholar
    • Export Citation
  • Betts, A. K., , M. Köhler, , and Y. Zhang, 2009: Comparison of river basin hydrometeorology in ERA-Interim and ERA-40 reanalyses with observations. J. Geophys. Res., 114, D02101, doi:10.1029/2008JD010761.

    • Search Google Scholar
    • Export Citation
  • Birkett, C. M., 1995: The contribution of TOPEX/Poseidon to the global monitoring of climatically sensitive lakes. J. Geophys. Res., 100, 25 17925 204.

    • Search Google Scholar
    • Export Citation
  • Birkett, C. M., 2000: Synergistic remote sensing of Lake Chad: Variability of basin inundation. Remote Sens. Environ., 72, 218236.

  • Birkett, C. M., , R. Murtugudde, , and T. Allan, 1999: Indian Ocean climate event brings floods to East Africa’s lakes and the Sudd Marsh. Geophys. Res. Lett., 26, 10311034.

    • Search Google Scholar
    • Export Citation
  • Birkett, C. M., , C. Reynolds, , B. Beckley, , and B. Doorn, 2010: From research to operations: The USDA global reservoir and lake monitor. Coastal Altimetry, Springer Publications, 19–50.

    • Search Google Scholar
    • Export Citation
  • Calder, R. I., , R. Hall, , H. Bastable, , H. Gunston, , O. Shela, , A. Chirwa, , and R. Kafundu, 1995: The impact of land use change on water resources in sub-Saharan Africa: A modeling study of Lake Malawi. J. Hydrol., 170, 123135.

    • Search Google Scholar
    • Export Citation
  • Calmant, S., , F. Seyler, , and J. F. Crétaux, 2008: Monitoring continental surface waters by satellite altimetry. Surv. Geophys., 29, 247269.

    • Search Google Scholar
    • Export Citation
  • Carmouze, J. P., , J. R. Durand, , and C. Leveque, 1983: The lacustrine ecosystem during the “Normal Chad” period and the drying phase. Lake Chad: Ecology and Productivity of a Shallow Tropical Ecosystem,Monogr. Biol., Vol. 53, Dr. W. Junk Publishers, 527–560.

    • Search Google Scholar
    • Export Citation
  • Charney, J. G., 1969: The intertropical convergence zone and the Hadley circulation of the atmosphere. Proc. WMO/IUGG Symp. on Numerical Weather Prediction, Tokyo, Japan, Japanese Meteorological Agency, 73–79.

    • Search Google Scholar
    • Export Citation
  • Coe, M. T., , and C. M. Birkett, 2004: Calculation of river discharge and prediction of lake height from satellite radar altimetry: Example for the Lake Chad basin. Water Resour. Res., 40, W10205, doi:10.1029/2003WR002543.

    • Search Google Scholar
    • Export Citation
  • Crétaux, J.-F., , and C. Birkett, 2006: Lake studies from satellite radar altimetry. C. R. Geosci., 338, 10981112.

  • Crétaux, J.-F., and Coauthors, 2011: SOLS: A lake database to monitor in the near real time water level and storage variations from remote sensing data. Adv. Space Res., 47, 14971507.

    • Search Google Scholar
    • Export Citation
  • Fearnside, P. M., 1989: Brazil’s Balbina Dam: Environment versus the legacy of the pharaohs in Amazonia. Environ. Manage., 13, 401423.

    • Search Google Scholar
    • Export Citation
  • Glantz, M. H., , R. W. Katz, , and N. Nicholls, 1991: Teleconnections Linking Worldwide Climate Anomalies: Scientific Basis and Societal Impact. Cambridge University Press, 535 pp.

    • Search Google Scholar
    • Export Citation
  • Guyot, J. L., , M. A. Roche, , L. Noriega, , H. Calle, , and J. Quintanilla, 1990: Salinities and sediment transport in the Bolivian Highlands. J. Hydrol., 113, 147162.

    • Search Google Scholar
    • Export Citation
  • Hughes, R. H., , and J. S. Hughes, 1992: A Directory of African Wetlands. IUCN, 820 pp.

  • Inomata, H., , and K. Fukami, 2008: Restoration of historical hydrological data of Tonle Sap Lake and its surrounding areas. Hydrol. Processes, 22, 13371350.

    • Search Google Scholar
    • Export Citation
  • International Lake Environment Committee, cited 1986: The United Nations Environment Program and Environment Agency, Government of Japan. World Lakes Database. [Available online at http://www.ilec.or.jp/database/database_old.html.]

    • Search Google Scholar
    • Export Citation
  • Isiorho, S. A., , G. Matisoff, , and K. S. Wehn, 1996: Seepage relationships between Lake Chad and the Chad aquifer. Ground Water, 34, 819826.

    • Search Google Scholar
    • Export Citation
  • Janowiak, J. E., 1988: An investigation of interannual rainfall variability in Africa. J. Climate, 1, 240255.

  • Jimoh, O. D., 2008: Optimized operation of Kainji Reservoir. J. Technol., 12, 3442.

  • Kebede, S., , Y. Travi, , T. Alemayehu, , and V. Marc, 2006: Water balance of Lake Tana and its sensitivity to fluctuations in rainfall, Blue Nile basin, Ethiopia. J. Hydrol., 316, 233247.

    • Search Google Scholar
    • Export Citation
  • LakeNet, cited 1997: World lakes network. [Available online at http://www.worldlakes.org/.]

  • Magaña, V., , J. A. Amador, , and S. Medina, 1999: The midsummer drought over Mexico and Central America. J. Climate, 12, 15771588.

  • Magome, J., , H. Ishidaira, , and K. Takeuchi, 2004: Monitoring water storage variation in Lake Tonle Sap by satellite for water resources management. Proc. Int. Conf. on Advances in Integrated Mekong River Management, Vientiane, Laos, Mekong River Commission, 335–338.

    • Search Google Scholar
    • Export Citation
  • Marengo, J. A., and Coauthors, 2008: The drought of Amazonia in 2005. J. Climate, 21, 495516.

  • Mekong River Commission, 2005: Overview of the Hydrology of the Mekong Basin. Mekong River Commission, 73 pp.

  • Mercier, F., , A. Cazenave, , and C. Maheu, 2002: Interannual lake level fluctuations (1993–1999) in Africa from TOPEX/Poseidon: Connections with ocean–atmosphere interactions over the Indian Ocean. Global Planet. Change, 32, 141163.

    • Search Google Scholar
    • Export Citation
  • Murtugudde, R., , J. P. McCreary, , and A. J. Busalacchi, 2000: Oceanic processes associated with anomalous events in the Indian Ocean with relevance to 1997–1998. J. Geophys. Res., 105, 32953306.

    • Search Google Scholar
    • Export Citation
  • Nicholson, S. E., , and J. Kim, 1997: The relationship of the El Niño–Southern Oscillation to African rainfall. Int. J. Climatol., 17, 117135.

    • Search Google Scholar
    • Export Citation
  • Nicholson, S. E., , X. Yin, , and M. B. Ba, 2000: On the feasibility of using lake water balance model to infer rainfall: An example from Lake Victoria. Hydrol. Sci. J., 45, 7595.

    • Search Google Scholar
    • Export Citation
  • Nicholson, S. E., and Coauthors, 2003: Validation of TRMM and other rainfall estimates with a high-density gauge dataset for West Africa. Part II: Validation of TRMM rainfall products. J. Appl. Meteor., 42, 13551368.

    • Search Google Scholar
    • Export Citation
  • Roche, M. A., , J. Bourges, , J. Cortes, , and R. Mattos, 1992: Climatology and hydrology of the Lake Titicaca basin. Lake Titicaca: A Synthesis of Limnological Knowledge,Monogr. Biol., Vol. 68, Kluwer Academic Publishers, 63–88.

    • Search Google Scholar
    • Export Citation
  • Ropelewski, C. F., , and M. S. Halpert, 1996: Quantifying Southern Oscillation–precipitation relationships. J. Climate, 9, 10431059.

  • Simmons, A., , S. Uppala, , and D. Dee, 2007a: Update on ERA-Interim. ECMWF Newsletter, No. 111, ECMWF, Reading, United Kingdom, 5.

  • Simmons, A., , S. Uppala, , D. Dee, , and S. Kobayashi, 2007b: ERA-Interim: New ECMWF reanalysis products from 1989 onwards. ECMWF Newsletter, No. 110, ECMWF, Reading, United Kingdom, 25–35.

    • Search Google Scholar
    • Export Citation
  • Sombroek, W. G., 2001: Spatial and temporal patterns of Amazonian rainfall: Consequences for the planning of agricultural occupation and the protection of primary forests. Ambio, 30, 388396.

    • Search Google Scholar
    • Export Citation
  • Tonle Sap Biosphere Reserve Secretariat, cited 2006: Tonle Sap Biosphere Reserve (TSBR) environmental information database. [Available online at http://www.tsbr-ed.org/english/default.asp.]

    • Search Google Scholar
    • Export Citation
  • Uppala, S., and Coauthors, 2004: ERA-40: ECMWF 45-year reanalysis of the global atmosphere and surface conditions 1957–2002. ECMWF Newsletter, No. 101, ECMWF, Reading, United Kingdom, 2–21.

    • Search Google Scholar
    • Export Citation
  • Uppala, S., , D. Dee, , S. Kobayashi, , P. Berrisford, , and A. Simmons, 2008: Towards a climate data assimilation system: Status update of ERA-Interim. ECMWF Newsletter, No. 115, ECMWF, Reading, United Kingdom, 12–18.

    • Search Google Scholar
    • Export Citation
  • Vallet-Coulomb, C., , D. Legesse, , G. Gasse, , Y. Travi, , and T. Chernet, 2001: Lake evaporation estimates in tropical Africa (Lake Ziway, Ethiopia). J. Hydrol., 245, 117.

    • Search Google Scholar
    • Export Citation
  • Van Campo, E., , and F. Gasse, 1993: Pollen- and diatom-inferred climatic and hydrological changes in Sumxi Co basin (Western Tibet) since 13 000 yr B.P. Quat. Res., 39, 300313.

    • Search Google Scholar
    • Export Citation
  • Vijverberg, J., , F. A. Sibbing, , and E. Dejen, 2009: Lake Tana: Source of the Blue Nile. The Nile: Origin, Environments, Limnology and Human Use,Monogr. Biol., Vol. 89, Springer, 163–192.

    • Search Google Scholar
    • Export Citation
  • Xie, P., , J. E. Janowiak, , P. A. Arkin, , R. F. Adler, , A. Gruber, , R. R. Ferraro, , G. J. Huffman, , and S. Curtis, 2003: GPCP pentad precipitation analyses: An experimental dataset based on gauge observations and satellite estimates. J. Climate, 16, 21972214.

    • Search Google Scholar
    • Export Citation
  • Xie, S. P., , and J. A. Carton, 2004: Tropical Atlantic variability: Patterns, mechanisms, and impacts. Earth Climate: The Ocean–Atmosphere Interaction,Geophys. Monogr., Vol. 147, Amer. Geophys. Union, 121–142.

    • Search Google Scholar
    • Export Citation
  • Yoo, J.-M., , and J. A. Carton, 1990: Annual and interannual variation of the freshwater budget in the tropical Atlantic and the Caribbean Sea. J. Phys. Oceanogr., 20, 831845.

    • Search Google Scholar
    • Export Citation
  • View in gallery

    Monthly distribution of rainfall (mm day−1) for selected tropical lakes and reservoirs (stars), with the standard deviation of climatological monthly rainfall shaded in the background. Solid black lines show climatological monthly GPCP rainfall averaged over the entire lake catchment basin, where vertical axes span 0–12.5 mm day−1, and horizontal axes span January–December. Dashed lines show annual mean of rainfall.

  • View in gallery

    Lake Malawi with many of its rivers (blue) and catchment basin (black) delineated. Outflow is through the Shire River at the southern end. Altimeter ground tracks overlaid: Envisat and ERS (gray); TOPEX/Poseidon (yellow); Jason-1(red).

  • View in gallery

    Rainfall and evaporation (mm day−1) estimates averaged over the Malawi catchment area for two years 2000–01: TRMM (dark blue), GPCP (light blue), and ERA-Interim rainfall (red), and ERA-Interim evaporation (red dotted).

  • View in gallery

    Scatter diagram of 5-day-average observed and modeled Lake Chad during 1997–2007 (when available) using TRMM rainfall with a 30-day lag. The scatter diagram clearly shows a quadratic component to the relationship predicted by Eq. (3) as the result of expansion of the lake surface area with rising lake level. The best-fit relationship, Model-T = 0.21H2 + 0.65H − 0.05, however, remains predominantly linear.

  • View in gallery

    Scatter diagram of 5-day-average observed lake level during 1993–2007 (when available): LEGOS vs GRLM lake-level estimates (m) for (a) Lake Malawi, correlation r = 0.99, and for (b) Reservoir Kainji, correlation r = 0.87.

  • View in gallery

    Scatter diagram of 5-day-average observed LEGOS vs modeled lake level (m) for Lake Malawi using rainfall from (a) ERA-Interim with a 25-day lag, (b) GPCP with a 15-day lag during 1993–2007, (c) TRMM, and (d) GPCP both with a 15-day lag during 1998–2007. At Malawi Model-I provides the best fit with the highest correlation r = 0.95.

  • View in gallery

    Using rainfall from ERA-Interim (gray line) and GPCP (black line) for Lake Malawi, (a) relationship between time delay of freshwater input and level rise (days) and correlation coefficient values, r, and (b) relationship between the effective catchment to lake area ratio and rms values during 1993–2007: (left) r values for ERA-Interim and for (right) GPCP. The maximum correlation is at 25-day lag for ERA-Interim and 15-day lag for GPCP and in (b) the lowest rms for the effective catchment to lake ratio (AC/AL)eff is ~3.

  • View in gallery

    Observed LEGOS (black) and modeled lake level (colored) for 12 lakes and reservoirs considered in this study: (a) ERA-Interim (red) and GPCP (blue) for time period 1992–2007 and (b) TRMM (red) and GPCP (blue) for time period 1998–2007. Displacement between horizontal lines is 3 m. Levels for two lakes, Turkana and Balbina, have been reduced in amplitude by a factor of 3 and 2, respectively, so as to include them in the same figure. A quadratic trend has been removed from each time series.

  • View in gallery

    Similar to Fig. 8, but with the annual and semiannual Fourier harmonics filtered out. Displacement between horizontal lines is 2 m. Levels for four lakes, Turkana, Tanganyika, Mweru, and Balbina, have been reduced in amplitude by a factor of 5, 1.5, 1.5, and 2.5, respectively, to include them in the same figure. Gray boxed areas identify two El Niño periods (1997–98, 2002–03).

All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 54 54 9
PDF Downloads 29 29 1

Climatic Effects on Lake Basins. Part I: Modeling Tropical Lake Levels

View More View Less
  • 1 Department of Atmospheric and Oceanic Science, University of Maryland, College Park, College Park, Maryland
  • | 2 Earth System Science Interdisciplinary Center, University of Maryland, College Park, College Park, Maryland
© Get Permissions
Full access

Abstract

The availability of satellite estimates of rainfall and lake levels offers exciting new opportunities to estimate the hydrologic properties of lake systems. Combined with simple basin models, connections to climatic variations can then be explored with a focus on a future ability to predict changes in storage volume for water resources or natural hazards concerns. This study examines the capability of a simple basin model to estimate variations in water level for 12 tropical lakes and reservoirs during a 16-yr remotely sensed observation period (1992–2007). The model is constructed with two empirical parameters: effective catchment to lake area ratio and time delay between freshwater flux and lake level response. Rainfall datasets, one reanalysis and two satellite-based observational products, and two radar-altimetry-derived lake level datasets are explored and cross checked. Good agreement is observed between the two lake level datasets with the lowest correlations occurring for the two small lakes Kainji and Tana (0.87 and 0.89). Fitting observations to the simple basin model provides a set of delay times between rainfall and level rise ranging up to 105 days and effective catchment to lake ratios ranging between 2 and 27. For 9 of 12 lakes and reservoirs the observational rainfall products provide a better fit to observed lake levels than the reanalysis rainfall product. But for most of the records any of the rainfall products provide reasonable lake level estimates, a result which opens up the possibility of using rainfall to create seasonal forecasts of future lake levels and hindcasts of past lake levels. The limitations of the observation sets and the two-parameter model are discussed.

Corresponding author address: James A. Carton, Dept. of Atmospheric and Oceanic Science, University of Maryland, College Park, MD 20742. E-mail: carton@atmos.umd.edu

Abstract

The availability of satellite estimates of rainfall and lake levels offers exciting new opportunities to estimate the hydrologic properties of lake systems. Combined with simple basin models, connections to climatic variations can then be explored with a focus on a future ability to predict changes in storage volume for water resources or natural hazards concerns. This study examines the capability of a simple basin model to estimate variations in water level for 12 tropical lakes and reservoirs during a 16-yr remotely sensed observation period (1992–2007). The model is constructed with two empirical parameters: effective catchment to lake area ratio and time delay between freshwater flux and lake level response. Rainfall datasets, one reanalysis and two satellite-based observational products, and two radar-altimetry-derived lake level datasets are explored and cross checked. Good agreement is observed between the two lake level datasets with the lowest correlations occurring for the two small lakes Kainji and Tana (0.87 and 0.89). Fitting observations to the simple basin model provides a set of delay times between rainfall and level rise ranging up to 105 days and effective catchment to lake ratios ranging between 2 and 27. For 9 of 12 lakes and reservoirs the observational rainfall products provide a better fit to observed lake levels than the reanalysis rainfall product. But for most of the records any of the rainfall products provide reasonable lake level estimates, a result which opens up the possibility of using rainfall to create seasonal forecasts of future lake levels and hindcasts of past lake levels. The limitations of the observation sets and the two-parameter model are discussed.

Corresponding author address: James A. Carton, Dept. of Atmospheric and Oceanic Science, University of Maryland, College Park, MD 20742. E-mail: carton@atmos.umd.edu

1. Introduction

Monitoring and predicting water availability plays a critical role in most parts of the world and particularly for the agrarian economies of the tropics (Glantz et al. 1991; Anyamba and Eastman 1996). In the past decade improvements in satellite radar altimeter estimates of river and lake levels offer an exciting additional monitoring tool to complement declining networks of in situ gauges (Crétaux and Birkett 2006; Anyah et al. 2006). However, prediction systems are currently limited since current climate models do not resolve detailed hydrologic processes at the level of individual lakes. Here we exploit the simultaneous availability of estimates of net surface freshwater flux and lake levels during a 16-yr altimetric satellite observation period (1992–2007) to develop simple models of water level variation for a sample of tropical lakes. The results of this study provide information on the values of the effective catchment to lake ratios and the time delay between freshwater flux and lake level response, allowing us to compare the consistency of independent rainfall and lake level observations. While we focus on tropical lakes because of their strong seasonal and interesting interannual variability, the ideas should be applicable to lakes at higher latitudes as well.

Net surface freshwater flux is the difference between precipitation and evaporation over the catchment area. In the tropics net freshwater flux varies strongly seasonally, mainly as a result of seasonal variations in rainfall rather than evaporation. On monthly time scales the spatial distribution of rainfall is concentrated in atmospheric convergence zones where rainfall exceeds 10 mm day−1. The principal convergence zones are the intertropical convergence zone (ITCZ), and its intersection with tropical continents, the South Pacific and Atlantic convergence zones. Of these, the narrow zonally oriented ITCZ gives rise to the most striking variations in rainfall as it follows the seasonal shift of solar declination northward in boreal summer and southward in austral summer (Charney 1969), and its movements are thus responsible for the wet and dry seasons in the tropics.

Near the annual mean position of the ITCZ (generally a few degrees north of the equator) freshwater input reaches a peak twice a year in boreal spring and boreal fall, as the ITCZ passes overhead on both its northward and southward migrations. The distribution of regions with these semiannual rainy seasons is somewhat irregular spatially, particularly in the Amazon region (Sombroek 2001; Marengo et al. 2008). Farther poleward the seasonal rainfall is characterized by one wet season in the northern tropics during boreal summer and in the southern tropics during boreal winter.

In addition to seasonal variations, ITCZ rainfall exhibits strong interannual variability, notably associated with ENSO. During the northern winter of the warm El Niño phase of ENSO rainfall is enhanced in the central and eastern tropical Pacific as well as eastern tropical Africa, while drought conditions prevail in maritime Australasia and in eastern equatorial South America (Ropelewski and Halpert 1996; Nicholson and Kim 1997). By the northern summer of an El Niño year dry conditions extend throughout northern tropical South America, while the Indian monsoon is reduced in strength. During the cool La Niña phase precipitation patterns are approximately reversed, with dry conditions in the central and eastern tropical Pacific and eastern Africa and anomalously wet conditions in maritime Australasia in northern winter. By the following summer anomalously wet conditions span northern South America as well as India (due to a strengthening of the Indian monsoon). During our 16-yr period of interest there were five El Niño events: a strong and long-lasting event in 1997–98, substantial events in 1992–93 and 2002–03, less substantial events in 1994–95 and 2006–07, and three La Niña events in 1998–99, 1999–2000, and 2007–08.

In addition to ENSO, the tropics support several other identifiable sources of climate variability affecting rainfall distributions. The Indian sector undergoes zonal shifts of rainfall on interannual time scales forming a dipole pattern in anomalous rainfall (Ashok et al. 2001). An extremely strong negative phase of this pattern occurred in 1997–98 during which East African rainfall, usually only slightly higher during an El Niño event, was very severe, while Indonesia experienced droughts. Indeed, the anomalous weather patterns during 1997–98 had a striking impact on the Rift Valley lakes of East Africa with an anomalous rainfall increase of 20%–160% during the rainy season (Birkett et al. 1999; Murtugudde et al. 2000; Mercier et al. 2002).

Rainfall in the tropical Atlantic sector is also subject to interannual and decadal variations. The Nordeste region of Brazil, located at the latitude of the southernmost position of the seasonal ITCZ, in certain years can be subject to extreme drought or rainfall anomalies (Xie and Carton 2004). Extreme rainfall years for this region include 1993, 1995 (high), and 1998 (low). Likewise, changes in the northernmost seasonal migration of the ITCZ leads to years of anomalous rainfall in the Sahel region of central and western North Africa (Janowiak 1988). Since 1991 this region has been anomalously dry, with only occasional years of above average rainfall including 1994, 1999, and 2003. This drying trend is evident at Lake Chad in central North Africa, where altimetry observations, reviewed below, show that the water level has declined by more than 0.5 m during the past nine years.

Beginning in the early 1990s the launch of a succession of satellite radar altimeters has opened up the potential of remote sensing of levels for those lakes crossed by satellite repeat tracks. Initially poor signal-to-noise ratios limited the use of this data. However, improvements in processing techniques have dramatically improved the accuracy of this data (Birkett 1995), and the availability of multiple satellites in different orbits has increased the number of lakes covered as well as the number of measurements.

In this study we focus on tropical lakes and reservoirs in the band of latitudes swept seasonally by movements of the ITCZ. In addition to providing strong rain-induced level variations, their tropical locations preclude concerns about radar scattering by ice and level changes due to seasonal thermal expansion. We focus on a sample of 12 tropical lakes and reservoirs distributed across three continents: 8 in Africa, 3 in Central and South America, and 1 in Southeast Asia (Table 1) for which acceptable multidecadal records are available. Most of these lakes and reservoirs are controlled to some extent. However, the impact of management is probably largest for the three reservoirs (Kainji, Bangweulu, and Balbina). Indeed, most reservoirs are multipurpose; as well as for irrigation, hydropower, and flood control, they are used for water supply, navigation, fishing, and recreation (Avakyan and Iakovleva 1998). Unfortunately, small lakes (<100 km2) generally are not sampled sufficiently by the altimetry and thus cannot be included in this study.

Table 1.

Geographical characteristics of the lakes and reservoirs considered in this study. Surface and volume areas are variable with time and seasons.

Table 1.

Hydrologic models developed for lake hydrological systems are of two types. The first includes the complex physically based models developed as a result of considerations of detailed hydrology, storage, and transport mechanisms. The second type, considered here, are simplified empirical linear models, estimating lake level as a function of net freshwater flux into the catchment basin. In this study our simple basin model contains two parameters: effective catchment to lake area ratio and time delay, both of which are determined by linear regression based on the simultaneous availability of lake level and rainfall. Successful application of this type of model opens up the possibility of deriving lake levels from water flux observations or forecast models, extending the link between these different components of the hydrologic system.

2. Study regions

Many of the African lakes that we consider here (listed in Table 1) lie in the Rift Valley of eastern and central Africa, including Turkana, Tanganyika, Mweru, Bangweulu, and Malawi. Three Western Rift Valley lakes—Tanganyika, Mweru, and Bangweulu—are part of the Congo River basin. Lake Tanganyika is the world’s second or third largest lake by volume and second in depth, with major inputs from the Ruzizi and Malagarasi Rivers and major outflow into the Lukuga River. Bangweulu Reservoir has many sources, of which the Chambeshi River (the source of the Congo River) is the largest, but drains through the Luapula River. The Luapula River, together with the Kalungwishi River, provides water to tiny Lake Mweru. For all three of these Southern Hemisphere lakes the main rainy season is in boreal winter (Fig. 1).

Fig. 1.
Fig. 1.

Monthly distribution of rainfall (mm day−1) for selected tropical lakes and reservoirs (stars), with the standard deviation of climatological monthly rainfall shaded in the background. Solid black lines show climatological monthly GPCP rainfall averaged over the entire lake catchment basin, where vertical axes span 0–12.5 mm day−1, and horizontal axes span January–December. Dashed lines show annual mean of rainfall.

Citation: Journal of Climate 24, 12; 10.1175/2010JCLI3602.1

Two deep lakes, Malawi and Turkana, lie in the Eastern Rift Valley. Lake Malawi is 580 km long and is the most southern of the great African Rift Valley lakes. Located within the Zambezi River basin it is the second largest and second deepest lake in Africa. Supplied primarily by the Ruhuhu River, Lake Malawi drains into the Shire River. The smaller closed Lake Turkana has several source rivers in the Nile River basin. The main water input (90%) is from the Omo River, which enters the lake from the north. The second largest input is from the Turkwel River, which is in the process of being dammed for hydroelectric power generation. Lake Turkana water loss is through evaporation owing to its arid climate. It is the world’s largest permanent closed desert lake and the world’s largest alkaline lake. By volume it is also the world’s fourth largest salt lake. Seasonal rainfall for Malawi resembles that of the Western Rift Valley lakes described above, while Lake Turkana shows only weak seasonal rains due to shadowing by the surrounding terrain, with the highest rainfall coming during the “long rains” of March–June.

The last three African lakes that we consider are Lake Tana, which lies north of Turkana in the Ethiopian Rift Valley; Lake Chad, in central North Africa; and the Kainji Reservoir, positioned southwest from Lake Chad, with the main rainy season in boreal summer (Fig. 1). Lake Tana, the source of the Blue Nile, is fed by four rivers and numerous seasonal streams. With a mean depth of only 8 m, the strong seasonal cycle of rain drives a 25% seasonal variation in depth; however, construction of a weir in 1996 has limited fluctuations of the level of this lake (Kebede et al. 2006).

Shallow (<7 m) Lake Chad experiences seasonal level fluctuations in the lake and surrounding marsh area, expanding in size from about 2000 km2 to about 15 000 km2 between dry and wet seasons. Lake Chad receives most of its water (95%) from the Chari/Logone River system, which connects Chad to the seasonally rainy highlands to the south with similar timing but half the amplitude of Kainji Reservoir and Lake Tana (Van Campo and Gasse 1993). Most water loss is through evaporation and water extraction, though it has ~15% water loss through ground seepage (Carmouze et al. 1983; Isiorho et al. 1996). Declining rains and excess water extraction have been held jointly responsible for the shrinkage of the lake over the past half century.

Lake Chad was the subject of earlier altimeter level studies by Coe and Birkett (2004) who developed a predictive model based on correlating upstream water levels in the Chari River with downstream levels in the lake. Estimates of phase lags across the basin varied from 20 days to 5 months (Birkett 2000; Coe and Birkett 2004); however, a one-month phase lag between the lake and the Chari River was explored as a potential warning tool of high flows.

The Kainji Dam was commissioned in December 1968, forming the Kainji Reservoir for the purpose of generating electricity. Incidentally, there are problems associated with its operation. During high September inflows there is often annual flooding of the lower Niger plains as the spillways are opened. During periods of low inflows (March–May), the water level is often well below the desired operational level (Jimoh 2008).

In Central and South America we consider three lakes: Lake Titicaca, the largest freshwater lake in South America; Balbina Reservoir in central Amazonia; and Lake Nicaragua, the largest lake in Central America. Lake Titicaca is fed by rainfall and meltwater from mountain snowfields. Most water loss is through evaporation, although about 10% is lost through the Desaguadero River (Roche et al. 1992). The water level of Lake Titicaca undergoes decadal variations of 1–2 m owing to changes in rainfall. For example, it experienced low water levels in the 1940s but rising elevations in recent years (Guyot et al. 1990). Lake Titicaca, because of its Southern Hemisphere location, experiences a rainy season in boreal winter (Fig. 1).

Shallow Balbina Reservoir was created in 1987 by damming the Uatumã River in the Amazon basin to supply hydroelectric power. Reservoir level variations reflect variations of rainfall into the Amazon basin with highest rain from February through May (with peak rain in March–April). It contains 1500 islands and innumerable stagnant bays where the water’s residence time can exceed the 1-yr average (Fearnside 1989).

Lake Nicaragua, located in Central America and affected by rainfall from the eastern Pacific ITCZ, experiences two rainy seasons per year and a relative minimum of rainfall during July and August known as the midsummer drought (Magaña et al. 1999). In response, Lake Nicaragua has a twice-yearly peak of lake level (Fig. 1).

Lake Tonle Sap in Cambodia is the largest lake in Southeast Asia and a key part of the Mekong hydrological system. It has only one major inlet/outlet—the Mekong River. Water drains from Tonle Sap into the Mekong through Tonle Sap River beginning in September. By spring Tonle Sap has an average depth of only 1 m. The onset of the monsoon season in late May and the resulting rise in Mekong River water levels reverses the direction of Tonle Sap River and Lake Tonle Sap begins to flood, quadrupling its surface area and deepening it to up to 9 m. Large changes in the area of Lake Tonle Sap mean that its volume depends on both lake level and surface area with the area expanding at a rate of ~1000 km2 m−1 rise of level (Magome et al. 2004; Mekong River Commission 2005). The lake is also subject to year-to-year variations. For example, Inomata and Fukami (2008) point out that 1998 was a year of unusually low rainfall, which consequently resulted in an anomalously low lake level.

3. Datasets

This study utilizes five different datasets focusing on two main parameters: lake level and rainfall. Lake level variability is determined by satellite radar altimeters. TOPEX/Poseidon (T/P) (1992–2002) and Jason-1 (2002–08) have a 10-day repeat cycle with a track spacing of 350 km at the equator. Validation exercises with ground-based gauge data have shown that the time series of lake level variations can be accurate to 3 cm. The Geosat Follow-on (GFO) Mission (2000–08) has a 17-day repeat cycle and 170-km equatorial track spacing with accuracies 3.5 cm rms. The Earth Resources Satellites ERS-1 (1991–96), ERS-2 (1995–2002), and Envisat (2002–present) follow a 35-day repeat cycle with 80-km equatorial track spacing and accuracies generally 9 cm rms. All satellites require a minimum target area >100 km2 or width >500 m to achieve sufficient data quality (Crétaux and Birkett 2006). Some lakes such as Lake Malawi are crossed by multiple tracks (Fig. 2). Others, such as Lake Tonle Sap, are crossed only by one track, in this case near the outlet to the south of the lake.

Fig. 2.
Fig. 2.

Lake Malawi with many of its rivers (blue) and catchment basin (black) delineated. Outflow is through the Shire River at the southern end. Altimeter ground tracks overlaid: Envisat and ERS (gray); TOPEX/Poseidon (yellow); Jason-1(red).

Citation: Journal of Climate 24, 12; 10.1175/2010JCLI3602.1

In addition to the availability of tracks, data retrievals over lakes are subject to coastline and island interference. The accuracy of the altimetric height lake level is also affected by lake size and the number of available radar echoes collected, the surface roughness of the water (wave height), as well as atmospheric parameters such as water vapor. Due to the presence of on-board radar echo filtering software, lake level observations from Jason-1 are particularly poor for the smaller or more sheltered lakes with calm waters. A full discussion of the error budget terms is provided in Crétaux and Birkett (2006) and Calmant et al. (2008). We note here that, in general, comparison of the combined altimeter record to gauges and intercomparison of measurements between instruments suggest the level estimates for large lakes are generally accurate to within 5 cm, but this level of accuracy may degrade to tens of centimeters (e.g., Lake Chad, Birkett 2000) to over a meter (e.g., narrow reservoirs such as Lake Powell) depending on the target (Birkett et al. 2010).

For 11 of our 12 lakes and reservoirs we use the merged-satellite product of the Laboratoire d’Etudes en Géophysique et Océanographie Spatiales (LEGOS) (Crétaux et al. 2011). This merged product includes data from six satellites (T/P, Jason-1, ERS-1–2, ENVISAT, and GFO) with each dataset processed independently and intersatellite height biases removed using T/P data as a reference. The merged product is available at approximately monthly resolution starting in late September or early October 1992 for most lakes. For a few lakes, such as Bangweulu and Titicaca, the product begins in 2000. For Balbina Reservoir and Lake Tonle Sap the LEGOS product ends in 2002 coincident with the demise of T/P. We explore uncertainties due to altimeter sampling and processing by comparing the LEGOS data for eight of the lakes with corresponding level estimates available from the U. S. Department of Agriculture Foreign Agriculture Service, Global Reservoir and Lake Monitor (GRLM) (Birkett et al. 2010). The GRLM product is based only on three satellites—T/P, Jason-1, and GFO—but is available at finer 10-day resolution. For the comparison we interpolate both products to a uniform 5-day interval starting on the same dates, remove data outliers (identified subjectively), and fill short gaps in the time series by linear interpolation.

In this study we consider three rainfall products: the updated European Centre for Medium Range Weather Forecasts (ECMWF) ERA-Interim reanalysis (Simmons et al. 2007a,b; Uppala et al. 2008), the Global Precipitation Climatology Project (GPCP) pentad rainfall (Xie et al. 2003), and the Tropical Rainfall Measurement Mission (TRMM) 3B42 (V6) daily precipitation index (Adler et al. 2000). ERA-Interim rainfall, derived here from the 3-h time step forecasts from the 0000 UTC analysis at 1.5° spatial resolution, represents an update of the earlier 40-yr ECMWF Re-Analysis (ERA-40) (Uppala et al. 2004), created to address systematic errors in this earlier reanalysis. Over tropical land areas the ERA-Interim rainfall is slightly heavier (in general up to 3 mm day−1) than in the previous reanalysis (Uppala et al. 2008). In particular Betts et al. (2009) reports significant improvements of ERA-Interim rainfall over the Amazon basin, showing more rainfall in all seasons than ERA-40 (up to 1 mm day−1) but with an annual cycle that is still too weak.

The two observation-based products that we consider, GPCP and TRMM, both include satellite-based observations. GPCP is a combined surface rain gauge–satellite analysis available as a 5-day (pentad) average product at 2.5° spatial resolution. TRMM multisatellite precipitation analysis (TMPA) is an adjusted satellite analysis combining active and passive observations from the TRMM satellite together with more frequent geostationary IR measurements to obtain a calibrated product with high temporal sampling, available daily at 0.5° spatial resolution. GPCP is available for our full period of interest, while TRMM begins in 1998. Although TRMM and GPCP have very similar spatial and temporal patterns, over land TRMM has higher amplitude (Adler et al. 2000). A 1-yr comparison to rain gauges in northwest Africa by Nicholson et al. (2003) suggests that TRMM is nearly unbiased with a rms error, when smoothed to monthly resolution, comparable to GPCP. The differences among the rainfall products are illustrated in Fig. 3 for Lake Malawi. There it is evident that intraseasonal variations of GPCP and TRMM are larger than those of ERA-Interim; however, the seasonal cycles are similar to within 10%–20%.

Fig. 3.
Fig. 3.

Rainfall and evaporation (mm day−1) estimates averaged over the Malawi catchment area for two years 2000–01: TRMM (dark blue), GPCP (light blue), and ERA-Interim rainfall (red), and ERA-Interim evaporation (red dotted).

Citation: Journal of Climate 24, 12; 10.1175/2010JCLI3602.1

We consider only a single evaporation product, that of the ERA-Interim reanalysis. In the tropics evaporation has much weaker variations than precipitation (Yoo and Carton 1990), as illustrated at Lake Malawi (Fig. 3). Thus, in the tropics seasonal and interannual estimates of net freshwater flux are insensitive to the precision of the evaporation estimates.

4. Model

Here we introduce a simple water balance model similar to those used elsewhere (e.g., Calder et al. 1995; Nicholson et al. 2000; Vallet-Coulomb et al. 2001; Kebede et al. 2006). Invoking conservation of mass for a lake catchment system leads to an approximate relationship between the lake level anomaly from its time mean (H), lake area (AL), catchment area (AC), anomalous net freshwater flux , and anomalous water loss (εt) through a variety of processes at any given time (t) and space (x, y):
e1
Here we assume a single constant delay (δt) between the time of freshwater flux and the accumulation of water in the lake. Thermal expansion effects are neglected as, for example, are the effects of changing salinity on evaporation rates. If we assume water level does not vary spatially within the lake (which could occur owing to wind effects for example), compute the time average of (1), subtract that time average equation from (1), neglect water loss (εt = 0), and assume AC and AL are constant, then (1) reduces to the following predictive equation:
e2
where is the time-fluctuating anomaly of net freshwater flux from its time mean, averaged over the catchment basin, and similarly represents the time-fluctuating lake level anomaly about its mean [, see appendix]. We ignore anthropogenic influences, as we have no information to guide us on accounting for these effects.

The model contains two parameters: effective catchment to lake ratio, defined as the ratio of catchment area to lake area (AC/AL)eff computed by fitting (2) using observed height and freshwater flux data for each lake, and time delay between freshwater flux and lake level response (δt). These allow us to construct model estimates of lake level based solely on freshwater flux estimates. Any unmodeled drainage (e.g., groundwater seepage) is also folded into the definition of (AC/AL)eff. Note that (AC/AL)eff in general will differ from (AC/AL) as estimated from hydrologic drainage maps and the difference will provide information about the magnitude of unmodeled effects. The second parameter δt is estimated based on simultaneously maximizing the correlation between the model lake level and altimetric observations. Its uncertainty is determined by identifying the range of time delays spanned by the 95% confidence interval of the correlation. The resulting models are designated Model-I, Model-G, and Model-T for those developed using the three rainfall products (ERA-Interim, GPCP, and TRMM). Since the emphasis in this study (and the validity of the empirical model) is on interannual and shorter time scales, all time series are filtered to remove a least squares quadratic trend. Such trends could be introduced by unmodeled effects such as changes in land cover. However, the integral nature of the relationship between freshwater flux and lake level means that spurious trends in lake level may also be the result of white noise random errors in freshwater flux. By removing the trend we reduce the impacts of both model limitations and random error in the forcing.

For two shallow lakes, Chad and Tonle Sap, lake area increases dramatically with increasing lake level owing to the flooding of surrounding marshes. If instead of assuming a constant AL we assume a proportional relationship AL = QH, where Q is an empirical constant, then Eq. (2) leads to a square root relationship between the integral of freshwater flux and lake level:
e3
where (see appendix). When it is small compared to the variability of lake level we expect (3) to yield a quadratic relationship between and the rhs of (3). But, for deeper or more slowly expanding lakes we regain a linear relationship similar to that expressed in (2). For Lake Chad the scatter diagram in Fig. 4 presents the rhs of (3) plotted along the ordinate versus along the abscissa. The positive curvature in this relationship suggests that for this lake the second term on the lhs of (3) is not negligible compared to the first. However, the relationship remains approximately linear for the observed range of . Because of the appropriateness of a linear approximation for all lakes considered here we will only explore the linear model described by (2).
Fig. 4.
Fig. 4.

Scatter diagram of 5-day-average observed and modeled Lake Chad during 1997–2007 (when available) using TRMM rainfall with a 30-day lag. The scatter diagram clearly shows a quadratic component to the relationship predicted by Eq. (3) as the result of expansion of the lake surface area with rising lake level. The best-fit relationship, Model-T = 0.21H2 + 0.65H − 0.05, however, remains predominantly linear.

Citation: Journal of Climate 24, 12; 10.1175/2010JCLI3602.1

5. Results

a. Altimetry validation

Construction of lake-level time series involves a complex set of decisions regarding the choice of satellite, ground track, noise filtering algorithms, geophysical corrections, height reference datum, and application of intermission height bias. Since rather different choices have been made for LEGOS and GRLM, we begin by comparing the lake-level time series from the two different products for the eight lakes for which both altimetry datasets are available.

The comparison (after trend removal, described below) shows that the agreement is quite good for most lakes (Tables 2 and 3 show correlation and rms difference). Malawi, for example, shows excellent agreement with a correlation in excess of r = 0.99 (Fig. 5a) and a rms difference of 0.11 m. The worst agreement between the two lake level estimates occurs for Kainji Reservoir (r = 0.87 Fig. 5b), the smallest lake for which both datasets are available. Kainji Reservoir also has the largest rms difference between the estimates of 1.45 m, which is about half of the observed variability. In this respect it resembles Lakes Tana and Chad. The Lake Chad level is known to be difficult to estimate owing to the presence of shallow low-lying near-shore areas and islands. The causes of level error at Tana are less obvious. Determining the causes of these differences is complicated by the fact that LEGOS and GRLM use data from some of the same altimeters (but the estimates with range errors from individual satellites are not available for direct comparison). Thus, we are left to conclude simply that for most large lakes the products are in excellent agreement, but in the case of Kainji, Tana, and Chad there are significant differences between the LEGOS and GRLM estimates.

Table 2.

Correlation coefficient between observational and modeled height levels after removing the quadratic trend from the LEGOS observations and modeled height levels; and correlation coefficient between the two observational lake level analyses.

Table 2.
Table 3.

Rms difference between observational and modeled height levels (m) after removing the quadratic trend from the observations and modeled height levels; rms difference between the two observational lake-level analyses with the rms variability of the LEGOS lake levels.

Table 3.
Fig. 5.
Fig. 5.

Scatter diagram of 5-day-average observed lake level during 1993–2007 (when available): LEGOS vs GRLM lake-level estimates (m) for (a) Lake Malawi, correlation r = 0.99, and for (b) Reservoir Kainji, correlation r = 0.87.

Citation: Journal of Climate 24, 12; 10.1175/2010JCLI3602.1

b. Validation of model-based lake level estimates

We have pointed out that freshwater input to northern and southern tropical lakes peak in different seasons. Figure 1 shows the seasonal cycle of GPCP rainfall ranging from 0 to 12.5 mm day−1 with the standard deviation of climatological monthly rainfall (shaded in the background), in general, less than 2 mm day−1 for our selected tropical lakes and reservoirs. Rainfall is averaged over lake catchment areas defined and given in Table 1. Published estimates of the catchment and lake areas may vary with season and are different for different sources (the values we report in Table 1 are obtained from comparison of International Lake Environment Committee and LakeNet databases, with individual lake studies). For our catchment basins freshwater flux associated with GPCP rainfall is similar to TRMM and generally larger than ERA-Interim.

To illustrate our procedure for determining two model parameters (see Table 4) we consider Lake Malawi. For Lake Malawi setting δt = 15 day gives a correlation between left-hand and right-hand terms in Eq. (2) of r = 0.79 using GPCP rainfall, increasing to r = 0.95 when using ERA-Interim flux with δt = 25 day (Figs. 6a,b, Fig. 7). The uncertainty in the correlation associated with the relatively short data records leads to an estimate of the uncertainty in the time lag of ±10 day. Rms differences are also lower when using ERA-Interim rainfall rather than GPCP (0.24 m versus 0.33 m). During the shorter 11-yr period 1998 through 2007 when TRMM rainfall is available, TRMM flux gives r = 0.75, while GPCP leads to a better fit with r = 0.85 (Figs. 6c,d) and lower rms differences (0.24 m versus 0.32 m). Minimization of the rms differences leads to an effective catchment to lake area ratio of 3 regardless of the rainfall product used.

Table 4.

Model parameters: time lag δt (with uncertainty resulting from 95% confidence interval estimates) between lake level and integrated freshwater flux (in days), the effective catchment area to lake area ratio (AC/AL)eff, for the three models (Model-I, Model-G, and Model-T), and the actual ratio between catchment area to lake surface area (AC/AL). The AC and AL values for calculating AC/AL ratio are from Table 1.

Table 4.
Fig. 6.
Fig. 6.

Scatter diagram of 5-day-average observed LEGOS vs modeled lake level (m) for Lake Malawi using rainfall from (a) ERA-Interim with a 25-day lag, (b) GPCP with a 15-day lag during 1993–2007, (c) TRMM, and (d) GPCP both with a 15-day lag during 1998–2007. At Malawi Model-I provides the best fit with the highest correlation r = 0.95.

Citation: Journal of Climate 24, 12; 10.1175/2010JCLI3602.1

Fig. 7.
Fig. 7.

Using rainfall from ERA-Interim (gray line) and GPCP (black line) for Lake Malawi, (a) relationship between time delay of freshwater input and level rise (days) and correlation coefficient values, r, and (b) relationship between the effective catchment to lake area ratio and rms values during 1993–2007: (left) r values for ERA-Interim and for (right) GPCP. The maximum correlation is at 25-day lag for ERA-Interim and 15-day lag for GPCP and in (b) the lowest rms for the effective catchment to lake ratio (AC/AL)eff is ~3.

Citation: Journal of Climate 24, 12; 10.1175/2010JCLI3602.1

This procedure, carried out separately for each model, leads to time lag estimates of 0–15 days for Tana, Titicaca, and Nicaragua; 15–35 days for Tanganyika, Malawi, Chad, and Bangweulu; 45–100 days for Turkana, Mweru, and Kainji; while for Balbina and Tonle Sap there is no evident time lag between anomalous level rise and rainfall (Table 4). Some specific characteristics of the lakes might be used as explanations for these values of the empirical parameters: arid versus moist region, high versus low elevation, open versus closed basin, absolute size of the catchment basin (water coming to the lake from farther away takes longer), etc. Uncertainty in the estimate of time delay can be an important source of error as well. Our estimates of time lags are comparable to previous estimates where available. For example, for Lake Chad time lag varies from 20 days to 5 months according to Coe and Birkett (2004) and Birkett (2000), whereas our models show values ranging from 25 to 35 days.

Time series of lake levels and corresponding model estimates are shown in Figs. 8a,b. The variability of the lake-level height time series ranges over one order of magnitude among lakes because of differences in configurations and morphological characteristics of both the lakebeds and the catchment basins as well as rainfall variability.

Fig. 8.
Fig. 8.

Observed LEGOS (black) and modeled lake level (colored) for 12 lakes and reservoirs considered in this study: (a) ERA-Interim (red) and GPCP (blue) for time period 1992–2007 and (b) TRMM (red) and GPCP (blue) for time period 1998–2007. Displacement between horizontal lines is 3 m. Levels for two lakes, Turkana and Balbina, have been reduced in amplitude by a factor of 3 and 2, respectively, so as to include them in the same figure. A quadratic trend has been removed from each time series.

Citation: Journal of Climate 24, 12; 10.1175/2010JCLI3602.1

In response to the seasonal variations in rainfall, all lake levels, except for Lake Turkana, have prominent seasonal cycles. However, a few interesting differences between rainfall and lake level at seasonal time scales do occur. The seasonal cycle of ERA-Interim rainfall onto the Lake Chad catchment basin decreases in amplitude by 50% with time from 2001 to 2007 (0.64 to 0.33 m) in a way that is inconsistent with either the seasonal Lake Chad level variations or with either GPCP or TRMM rainfall, suggesting that ERA-Interim rainfall has an erroneous trend there. At Mweru, in contrast, seasonal ERA-Interim rainfall appears to increase in amplitude with time, especially during the recent period 2003–07 (increasing from 0.53 to 0.72 m). Lake Titicaca, high in the Andes, shows a reduced seasonal input of freshwater in the past few years, which does appear to be reflected in all rainfall estimates. At the Kainji Reservoir the modeled level has a very brief seasonal peak in rainfall in late summer (September). In contrast, the observed level remains high throughout the summer, perhaps as a result of active water management.

We next consider the accuracy of the three lake-level models (Tables 2 and 3). Because record lengths are shorter for Model-T, a version of Model-G (called Model-G2) is created, which is based on parameters determined from the same length record as Model-T and thus can be directly compared (Fig. 8b). The median correlation between the observed and modeled lake levels is slightly higher for Model-G than for Model-I (0.78 versus 0.70), and the median rms differences between observation and model are the same (0.45 m). Model-G2 has significantly higher correlation with observations than Model-T (0.84 versus 0.74), while the median rms difference is lower (0.30 m versus 0.41 m). However, a closer examination shows that the best model for a given lake varies. For Lake Chad and three Southern Rift Valley lakes—Tanganyika, Mweru, and Malawi—Model-I provides the better results (mean difference of 0.23) most of the time. For the remaining Southern Rift Valley Bangweulu Reservoir, all models do well overall (with correlations greater than 0.85). In contrast, for the Northern Rift Valley lakes Tana and Turkana, as well as the Central and South American lakes Nicaragua and Titicaca, Model-G provides the best results (mean difference of 0.39), while Model-T is slightly superior overall (mean difference of 0.05) for Balbina, Tonle Sap, and Kainji.

c. Effects of climate variability on tropical lake levels

To focus on year-to-year changes, we filter out the seasonal cycle by removing the annual and semiannual Fourier harmonics from both observed and modeled lake levels (experiments show these harmonics capture almost all the energy in the seasonal cycle).1 The anomaly time series are shown in Figs. 9a,b. With the seasonal cycle removed, the East African Rift Valley lakes—Turkana, Tanganyika, Mweru, and to a lesser extent Malawi—show pronounced rises of lake level in 1997–98 in response to the combined effects of El Niño and the positive phase of the Indian Ocean dipole, confirming results from direct lake level observations (Birkett et al. 1999; Murtugudde et al. 2000; Mercier et al. 2002). Western African Rift Valley lakes, such as Mweru and Tanganyika, also experience an enhanced lake level rise of 140%–190% during this anomalous rainy season. Interestingly, ERA-Interim shows a corresponding increase in rain into the Tanganyika and Mweru basins, which is not evident in GPCP, while GPCP shows an increase in rain into the Turkana catchment basin, which is not evident in ERA-Interim.

Fig. 9.
Fig. 9.

Similar to Fig. 8, but with the annual and semiannual Fourier harmonics filtered out. Displacement between horizontal lines is 2 m. Levels for four lakes, Turkana, Tanganyika, Mweru, and Balbina, have been reduced in amplitude by a factor of 5, 1.5, 1.5, and 2.5, respectively, to include them in the same figure. Gray boxed areas identify two El Niño periods (1997–98, 2002–03).

Citation: Journal of Climate 24, 12; 10.1175/2010JCLI3602.1

Lake Tonle Sap on the eastern side of the Indian Ocean dipole shows a corresponding decrease in level. We also confirm earlier observations of Alsdorf et al. (2001), showing that the South American Balbina Reservoir and the Central American Lake Nicaragua have 2-m and 1-m decreases in lake level during the spring and summer of 1998 resulting from the decrease in rainfall associated with the 1997–98 El Niño. Interestingly, the lake level responses to the 2002–03 El Niño are much less pronounced than the 1997–98 El Niño for most lakes. For example, Lake Nicaragua had peak values 0.47 m lower than the long-term average of height level. An exception was Lake Malawi, which had greater peak values (0.73 m) during the latter event perhaps because of climate variability in the Indian Ocean sector.

Strong tropical cyclones and hurricanes, as well as droughts, are noticeable in the lake level records. For example, Lake Nicaragua shows a dramatic 1-m increase in early November 1998 as a result of rainfall input from Hurricane Mitch (evident in GPCP and TRMM but not in ERA-Interim). Lake Nicaragua and much of Central America experienced a drought during late 2006 and early 2007. Similarly, the catchment basins of Lake Turkana and Lake Tana experienced major drought events during 2005 and 2007. Lake Nicaragua experienced a level drop during 2001 due to drought. Most lakes and reservoirs are also subject to active and variable water management, which likely plays a significant to dominant role in regulating water level.

6. Conclusions

This paper explores the use of a simple empirical model in deriving lake level estimates from rainfall. This type of model has a number of potential applications, including providing level estimates for basins where no ground-based or satellite-based level data is available and in developing lake level hindcasting/forecasting capabilities. It can be used by climate modelers and by the water management community, and thus potentially represents a significant contribution to earth system modeling. The model parameters (delay time and catchment to lake area ratio) also provide information regarding the hydrological properties of the lake basin.

We apply the model to compare the model-derived and altimeter lake-level time series for a sample set of 12 tropical lakes and reservoirs distributed across Africa, Asia, and the Americas, which lie in a band of strong seasonal monsoonal rainfall. The time series of the model and altimeter datasets span most or all of the 16-yr period 1992–2007. For eight of the lakes two different altimeter-based level products are available. One, LEGOS, is based on a combination of up to six altimeters, while the other, GRLM, is based on just three. The use of different altimeters and different ways the geophysical corrections and spatial filtering are carried out may affect the accuracy of the products. Yet, despite these differences the results from LEGOS and GRLM are reassuringly similar. The largest discrepancies between the two estimates occur for the two smallest lakes, Kainji and Tana, where the correlations dip slightly below 90%. For these two lakes the rms differences between the two level products are about half as large as the lake level variability itself, while for many of the other lakes the rms differences are less than 20% of the level variability.

All lake levels, except of Lake Turkana, have pronounced seasonal cycles with the largest amplitudes occurring for the lakes in high rainfall regions: Kainji in Africa, Balbina in South America, and Lake Tonle Sap in Southeast Asia. The lack of a seasonal cycle at Lake Turkana is due to its location in the rain shadowed region of the Chalbi Desert basin, blocked from the seasonal rains by its surrounding mountains. For the other lakes comparison of the timing and amplitude of the seasonal rainfall and lake level allows us to estimate model parameters, such as the time delay between freshwater input and level, and the effective catchment to lake area ratio. The ability to estimate these parameters is important since there are few published estimates of the former and published estimates of the latter vary widely. The lakes and reservoirs have time delays that range widely between 0 and 105 days with uncertainties of up to 35 days and effective catchment to lake ratios that range between 2 and 27.

The effective catchment to lake area ratios are generally larger than the estimated catchment to lake area ratios because of the presence of unresolved processes such as groundwater seepage, which is not otherwise accounted for in the simple model that we propose. An extreme example of groundwater seepage is Lake Chad, which has an estimated catchment to lake area ratio of 647 but an effective ratio of 10. Similarly, Lake Turkana has an estimated ratio of 20 but an effective ratio of 3.

For each lake or reservoir we construct a simple model of level anomaly forced by observed anomalous freshwater flux falling onto the associated catchment basin. Since freshwater flux variability in this latitude band is largely driven by rainfall variability, and analyses differ, we compare three: ERA-Interim reanalysis (Model-I), a combined rainfall analysis, GPCP (Model-G), and a purely satellite rainfall analysis, TRMM (Model-T). All three analyses are available at 5-times-daily resolution; however the TRMM rainfall is only available from 1998, while the other two span our full time period of interest (1992–2007). Either of the rainfall analyses provides reasonable lake level estimates for most lakes much of the time, but in some years the model fails at some locations. Many lakes show decadal trends, which may be caused by nonrainfall-related changes such as deforestation, growth of cultivated farming, irrigation, etc. To focus only on the (hopefully more rainfall-related) intraseasonal-to-interannual signals all records are filtered to remove a quadratic trend.

When the seasonal cycle is also removed, some of the time series reveal striking nonseasonal variability. The Rift Valley lakes, Turkana, Tanganyika, Mweru, and Malawi, all show a dramatic rise in response to the combined 1997–98 El Niño and Indian Ocean dipole events. In contrast, the Central and South American lakes, Nicaragua and Balbina, show significant level decreases for the same time period. Interestingly, other ENSO events do not show nearly as pronounced a response. Other climate events, such as tropical cyclones and hurricanes and episodic droughts, also show up in lake level records. Changes in the effective catchment area because of irrigation, and other human intrusions, are important and have their influence on model results as well.

The development of lake-level models driven by rainfall also gives us a way to evaluate the accuracy of the rainfall products by using the lake catchment basins as if they are giant rain gauges. For some lakes the ERA-Interim reanalysis rainfall provides the most successful model estimates, for example, Lake Malawi (r = 0.95). However, for most other lakes the best results are obtained using the observation-based products: GPCP or TRMM. For most of these lakes GPCP seems to produce superior results (with the median correlation of 0.78 versus 0.70 for ERA-Interim and 0.84 versus 0.74 for TRMM at two examined periods). The comparison of modeled and observed level allows us to identify weaknesses in the reanalysis rainfall estimates for particular catchment basins such as the weakening of the seasonal cycle with time at Lake Chad and the spurious interannual variability at Kainji Reservoir (ERA-Interim).

Simplifications inherent in the simple empirical model used here likely explain much of the mismatch between the model predictions and observations. To give just a few examples, this model neglects the possibility of multiple time scales associated with the delay between rainfall and changes in lake level. It assumes that the catchment basin remains static with time and neglects thermal expansion and ice formation, as well as the possibility of seasonal changes in land use. Many lakes and reservoirs are actively managed and yet this model provides no mechanism to reflect such management. The model is inherently linear and thus cannot adequately represent processes that are flow dependent such as lake discharge and groundwater seepage. Another important simplification is the lack of any model of the changing slope of water across the lake itself, important because the altimeter coverage may be quite limited for a given lake or, worse, may change with time as the satellite altimeters used in the analyses change. And of course the quality of the results will depend on the quality of surface flux estimates. Evaluating the impact of these simplifications and developing more sophisticated models should open up new avenues for research.

Still, despite the many simplifications associated with this two-parameter model, the reasonable values it produces suggest that historical rainfall estimates can provide an interesting way of evaluating past lake level variability, the reverse of the Nicholson et al. (2000) use of Lake Victoria gauge measurements to infer historical rainfall. Examination of the model errors may help to quantify anthropogenic effects like changing deforestation or irrigation where other sources of information may be limited. Finally, as noted in the introduction, the success of the models suggests their potential use for forecasting of lake levels in the medium range (1–3 weeks) based on output from weather prediction center forecast models. Exploring this possibility is the subject of our current research.

Acknowledgments

Data used in this study was provided by the Laboratoire d’Etudes en Géophysique et Océanographie Spatiales; the United States Department of Agriculture Foreign Agriculture Service, Global Reservoir and Lake Monitor database; the European Center for Medium Range Weather Forecasts; the Global Precipitation Climatology Project; and the Tropical Rainfall Measurement Mission. We gratefully acknowledge help and advice from John Janowiak and Phil Arkin. Support for MR and JAC has been provided by the NASA Winds Program (JPL 50526-8118), while support for CMB has been provided by the NASA OSTM and Decision Support Programs NNX08AT88G and NNX08AM72G. This work forms part of the dissertation research of MR.

APPENDIX

Lake Model

Begin with
ea1
Assume H is independent of x and y, that AL does not vary in time, and set εt = 0. We will assume that we have first removed the time mean precipitation and evaporation before applying these terms to (A1) [e.g., ]. Compute the time average of each term in (A1):
ea1a
So, we can replace H in (A1) with its anomaly relative to the time mean
ea2
Integrating (A2) gives
ea3
where is the average precipitation falling on the catchment area. Alternatively, we could assume AL = QH(t) in which case (2) becomes
ea4
where now we need to write explicitly that . Define , and (A4) becomes
ea5
Note that (A5) implies that correlating
eqa1
with can yield either a linear or quadratic relationship depending on level variability to mean level, .

REFERENCES

  • Adler, R. F., , G. J. Huffman, , D. T. Bolvin, , S. Curtis, , and E. J. Nelkin, 2000: Tropical rainfall distributions determined using TRMM combined with other satellite and rain gauge information. J. Appl. Meteor., 39, 20072023.

    • Search Google Scholar
    • Export Citation
  • Alsdorf, D., , C. Birkett, , T. Dunne, , J. Melack, , and L. Hess, 2001: Water level changes in a large Amazon lake measured with spaceborne radar interferometry and altimetry. Geophys. Res. Lett., 28, 26712674.

    • Search Google Scholar
    • Export Citation
  • Anyah, R. O., , F. H. M. Semazzi, , and L. Xie, 2006: Simulated physical mechanisms associated with climate variability over Lake Victoria basin in East Africa. Mon. Wea. Rev., 134, 35883609.

    • Search Google Scholar
    • Export Citation
  • Anyamba, A., , and J. R. Eastman, 1996: Interannual variability of NDVI Africa and its relation to El Niño–Southern Oscillation. Int. J. Remote Sens., 1, 25332548.

    • Search Google Scholar
    • Export Citation
  • Ashok, K., , Z. Guan, , and T. Yamagata, 2001: Impact of the Indian Ocean dipole on the relationship between the Indian monsoon rainfall and ENSO. Geophys. Res. Lett., 28, 44994502.

    • Search Google Scholar
    • Export Citation
  • Avakyan, A. B., , and V. B. Iakovleva, 1998: Status of global reservoirs: The position in the late twentieth century. Lakes Reservoirs: Res. Manage., 3, 4552.

    • Search Google Scholar
    • Export Citation
  • Betts, A. K., , M. Köhler, , and Y. Zhang, 2009: Comparison of river basin hydrometeorology in ERA-Interim and ERA-40 reanalyses with observations. J. Geophys. Res., 114, D02101, doi:10.1029/2008JD010761.

    • Search Google Scholar
    • Export Citation
  • Birkett, C. M., 1995: The contribution of TOPEX/Poseidon to the global monitoring of climatically sensitive lakes. J. Geophys. Res., 100, 25 17925 204.

    • Search Google Scholar
    • Export Citation
  • Birkett, C. M., 2000: Synergistic remote sensing of Lake Chad: Variability of basin inundation. Remote Sens. Environ., 72, 218236.

  • Birkett, C. M., , R. Murtugudde, , and T. Allan, 1999: Indian Ocean climate event brings floods to East Africa’s lakes and the Sudd Marsh. Geophys. Res. Lett., 26, 10311034.

    • Search Google Scholar
    • Export Citation
  • Birkett, C. M., , C. Reynolds, , B. Beckley, , and B. Doorn, 2010: From research to operations: The USDA global reservoir and lake monitor. Coastal Altimetry, Springer Publications, 19–50.

    • Search Google Scholar
    • Export Citation
  • Calder, R. I., , R. Hall, , H. Bastable, , H. Gunston, , O. Shela, , A. Chirwa, , and R. Kafundu, 1995: The impact of land use change on water resources in sub-Saharan Africa: A modeling study of Lake Malawi. J. Hydrol., 170, 123135.

    • Search Google Scholar
    • Export Citation
  • Calmant, S., , F. Seyler, , and J. F. Crétaux, 2008: Monitoring continental surface waters by satellite altimetry. Surv. Geophys., 29, 247269.

    • Search Google Scholar
    • Export Citation
  • Carmouze, J. P., , J. R. Durand, , and C. Leveque, 1983: The lacustrine ecosystem during the “Normal Chad” period and the drying phase. Lake Chad: Ecology and Productivity of a Shallow Tropical Ecosystem,Monogr. Biol., Vol. 53, Dr. W. Junk Publishers, 527–560.

    • Search Google Scholar
    • Export Citation
  • Charney, J. G., 1969: The intertropical convergence zone and the Hadley circulation of the atmosphere. Proc. WMO/IUGG Symp. on Numerical Weather Prediction, Tokyo, Japan, Japanese Meteorological Agency, 73–79.

    • Search Google Scholar
    • Export Citation
  • Coe, M. T., , and C. M. Birkett, 2004: Calculation of river discharge and prediction of lake height from satellite radar altimetry: Example for the Lake Chad basin. Water Resour. Res., 40, W10205, doi:10.1029/2003WR002543.

    • Search Google Scholar
    • Export Citation
  • Crétaux, J.-F., , and C. Birkett, 2006: Lake studies from satellite radar altimetry. C. R. Geosci., 338, 10981112.

  • Crétaux, J.-F., and Coauthors, 2011: SOLS: A lake database to monitor in the near real time water level and storage variations from remote sensing data. Adv. Space Res., 47, 14971507.

    • Search Google Scholar
    • Export Citation
  • Fearnside, P. M., 1989: Brazil’s Balbina Dam: Environment versus the legacy of the pharaohs in Amazonia. Environ. Manage., 13, 401423.

    • Search Google Scholar
    • Export Citation
  • Glantz, M. H., , R. W. Katz, , and N. Nicholls, 1991: Teleconnections Linking Worldwide Climate Anomalies: Scientific Basis and Societal Impact. Cambridge University Press, 535 pp.

    • Search Google Scholar
    • Export Citation
  • Guyot, J. L., , M. A. Roche, , L. Noriega, , H. Calle, , and J. Quintanilla, 1990: Salinities and sediment transport in the Bolivian Highlands. J. Hydrol., 113, 147162.

    • Search Google Scholar
    • Export Citation
  • Hughes, R. H., , and J. S. Hughes, 1992: A Directory of African Wetlands. IUCN, 820 pp.

  • Inomata, H., , and K. Fukami, 2008: Restoration of historical hydrological data of Tonle Sap Lake and its surrounding areas. Hydrol. Processes, 22, 13371350.

    • Search Google Scholar
    • Export Citation
  • International Lake Environment Committee, cited 1986: The United Nations Environment Program and Environment Agency, Government of Japan. World Lakes Database. [Available online at http://www.ilec.or.jp/database/database_old.html.]

    • Search Google Scholar
    • Export Citation
  • Isiorho, S. A., , G. Matisoff, , and K. S. Wehn, 1996: Seepage relationships between Lake Chad and the Chad aquifer. Ground Water, 34, 819826.

    • Search Google Scholar
    • Export Citation
  • Janowiak, J. E., 1988: An investigation of interannual rainfall variability in Africa. J. Climate, 1, 240255.

  • Jimoh, O. D., 2008: Optimized operation of Kainji Reservoir. J. Technol., 12, 3442.

  • Kebede, S., , Y. Travi, , T. Alemayehu, , and V. Marc, 2006: Water balance of Lake Tana and its sensitivity to fluctuations in rainfall, Blue Nile basin, Ethiopia. J. Hydrol., 316, 233247.

    • Search Google Scholar
    • Export Citation
  • LakeNet, cited 1997: World lakes network. [Available online at http://www.worldlakes.org/.]

  • Magaña, V., , J. A. Amador, , and S. Medina, 1999: The midsummer drought over Mexico and Central America. J. Climate, 12, 15771588.

  • Magome, J., , H. Ishidaira, , and K. Takeuchi, 2004: Monitoring water storage variation in Lake Tonle Sap by satellite for water resources management. Proc. Int. Conf. on Advances in Integrated Mekong River Management, Vientiane, Laos, Mekong River Commission, 335–338.

    • Search Google Scholar
    • Export Citation
  • Marengo, J. A., and Coauthors, 2008: The drought of Amazonia in 2005. J. Climate, 21, 495516.

  • Mekong River Commission, 2005: Overview of the Hydrology of the Mekong Basin. Mekong River Commission, 73 pp.

  • Mercier, F., , A. Cazenave, , and C. Maheu, 2002: Interannual lake level fluctuations (1993–1999) in Africa from TOPEX/Poseidon: Connections with ocean–atmosphere interactions over the Indian Ocean. Global Planet. Change, 32, 141163.

    • Search Google Scholar
    • Export Citation
  • Murtugudde, R., , J. P. McCreary, , and A. J. Busalacchi, 2000: Oceanic processes associated with anomalous events in the Indian Ocean with relevance to 1997–1998. J. Geophys. Res., 105, 32953306.

    • Search Google Scholar
    • Export Citation
  • Nicholson, S. E., , and J. Kim, 1997: The relationship of the El Niño–Southern Oscillation to African rainfall. Int. J. Climatol., 17, 117135.

    • Search Google Scholar
    • Export Citation
  • Nicholson, S. E., , X. Yin, , and M. B. Ba, 2000: On the feasibility of using lake water balance model to infer rainfall: An example from Lake Victoria. Hydrol. Sci. J., 45, 7595.

    • Search Google Scholar
    • Export Citation
  • Nicholson, S. E., and Coauthors, 2003: Validation of TRMM and other rainfall estimates with a high-density gauge dataset for West Africa. Part II: Validation of TRMM rainfall products. J. Appl. Meteor., 42, 13551368.

    • Search Google Scholar
    • Export Citation
  • Roche, M. A., , J. Bourges, , J. Cortes, , and R. Mattos, 1992: Climatology and hydrology of the Lake Titicaca basin. Lake Titicaca: A Synthesis of Limnological Knowledge,Monogr. Biol., Vol. 68, Kluwer Academic Publishers, 63–88.

    • Search Google Scholar
    • Export Citation
  • Ropelewski, C. F., , and M. S. Halpert, 1996: Quantifying Southern Oscillation–precipitation relationships. J. Climate, 9, 10431059.

  • Simmons, A., , S. Uppala, , and D. Dee, 2007a: Update on ERA-Interim. ECMWF Newsletter, No. 111, ECMWF, Reading, United Kingdom, 5.

  • Simmons, A., , S. Uppala, , D. Dee, , and S. Kobayashi, 2007b: ERA-Interim: New ECMWF reanalysis products from 1989 onwards. ECMWF Newsletter, No. 110, ECMWF, Reading, United Kingdom, 25–35.

    • Search Google Scholar
    • Export Citation
  • Sombroek, W. G., 2001: Spatial and temporal patterns of Amazonian rainfall: Consequences for the planning of agricultural occupation and the protection of primary forests. Ambio, 30, 388396.

    • Search Google Scholar
    • Export Citation
  • Tonle Sap Biosphere Reserve Secretariat, cited 2006: Tonle Sap Biosphere Reserve (TSBR) environmental information database. [Available online at http://www.tsbr-ed.org/english/default.asp.]

    • Search Google Scholar
    • Export Citation
  • Uppala, S., and Coauthors, 2004: ERA-40: ECMWF 45-year reanalysis of the global atmosphere and surface conditions 1957–2002. ECMWF Newsletter, No. 101, ECMWF, Reading, United Kingdom, 2–21.

    • Search Google Scholar
    • Export Citation
  • Uppala, S., , D. Dee, , S. Kobayashi, , P. Berrisford, , and A. Simmons, 2008: Towards a climate data assimilation system: Status update of ERA-Interim. ECMWF Newsletter, No. 115, ECMWF, Reading, United Kingdom, 12–18.

    • Search Google Scholar
    • Export Citation
  • Vallet-Coulomb, C., , D. Legesse, , G. Gasse, , Y. Travi, , and T. Chernet, 2001: Lake evaporation estimates in tropical Africa (Lake Ziway, Ethiopia). J. Hydrol., 245, 117.

    • Search Google Scholar
    • Export Citation
  • Van Campo, E., , and F. Gasse, 1993: Pollen- and diatom-inferred climatic and hydrological changes in Sumxi Co basin (Western Tibet) since 13 000 yr B.P. Quat. Res., 39, 300313.

    • Search Google Scholar
    • Export Citation
  • Vijverberg, J., , F. A. Sibbing, , and E. Dejen, 2009: Lake Tana: Source of the Blue Nile. The Nile: Origin, Environments, Limnology and Human Use,Monogr. Biol., Vol. 89, Springer, 163–192.

    • Search Google Scholar
    • Export Citation
  • Xie, P., , J. E. Janowiak, , P. A. Arkin, , R. F. Adler, , A. Gruber, , R. R. Ferraro, , G. J. Huffman, , and S. Curtis, 2003: GPCP pentad precipitation analyses: An experimental dataset based on gauge observations and satellite estimates. J. Climate, 16, 21972214.

    • Search Google Scholar
    • Export Citation
  • Xie, S. P., , and J. A. Carton, 2004: Tropical Atlantic variability: Patterns, mechanisms, and impacts. Earth Climate: The Ocean–Atmosphere Interaction,Geophys. Monogr., Vol. 147, Amer. Geophys. Union, 121–142.

    • Search Google Scholar
    • Export Citation
  • Yoo, J.-M., , and J. A. Carton, 1990: Annual and interannual variation of the freshwater budget in the tropical Atlantic and the Caribbean Sea. J. Phys. Oceanogr., 20, 831845.

    • Search Google Scholar
    • Export Citation
1

Because the seasonal cycle of Model-I Lake Chad level weakens with time, Fourier filtering this model leaves residual seasonal cycles at the beginning and end of the record that are out of phase.

Save