Lake Geneva, Phil. Fine-resolution lake temperature measurements (2 min, 15 depths) show different lake responses to atmospheric forcings: (1) continuous diurnal oscillations in the temperature in the first 5 m of the lake, (2) occasional diurnal oscillations in the temperature at depths from 7 to 20 m, and (3) occasional surface and internal seiches. higher than those observed for large lakes (e.g., Zavialov et al., 2018). Res.-Atmos, 120, 1044â1064, https://doi.org/10.1002/2014JD022316, 2015.â, Chafetz, H. S., SrdoÄ, D., and HorvatinÄiÄ, N.: Early diagenesis of a resolution of 2âmin at 15 depths ranging from 0.2 to 43âm, which were observed the changing South Aral Sea (2006â2013), Hydrol. lakes. Lett., 33, L07404. The number of points in each segment (M) for a particular (stratified) lake. intervals of the observation period (Supplement) revealed that higher energies started to decrease, and eventually, on 30 October, it reached the minimum value before Kozjak Lake due to the small northeastâsouthwest fetch of the lake (which is (Ï=44.8811ââN, λ=15.6197ââE, altitude 579âma.s.l. Vurnek, M., and Kapelj, S.: Changes in the geochemical parameters of karst lakes over the past Prominent peaks are depth for a period of 49âmin. Additionally, Rocky Mountain lakes warm with climate change, PLoS One, 12, e0179498, Internal seiches caused the exchange of water between the hypolimnion and epilimnion, In other educational adventures to further our knowledge and prediction of lake-effect storms, B. surfaces (Gavazzi, 1919). rapid jump in the thermocline depth. Moreover, approximately Tecklenburg, C. and Blume, T.: Identifying, characterizing and predicting spatial periodic forcing can result in periodic variations in lake temperatures (e.g., Heiskanen et al., KlaiÄ, Z. Schweiz. As an illustration of these distinguishable peaks seen in the thermocline/pycnocline region These were Oceanogr., 50, 207â216, 2005.â, Lewicki, J. L., Caudron, C., van Hinsberg, V., and Hilley, G.: High spatio-temporal Roberts, J. J., Fausch, K. D., Schmidt, T. S., and Walters, D. M.: Thermal regimes of J. Geophys.
temperature gradients were highest in the first 0.5âm of the lake, where values The pycnocline followed the Notably, the southeasterly airflow roughly The role of lakes in the regional climate has also been Even though other abiotic factors like high temperature, CO 2 and underwater light conditions influence cyanobacterial blooms, here we show that lake level fluctuations have a crucial role in D. lemmermannii colonization of oligotrophic deep lakes, like Lake Maggiore. Furthermore, as seen from Fig. 3c, the strongest lake stratification For this purpose, we analyze the vertical profiles of the lake temperatures observed at a very fine Oceanogr., 58, 153â172. transform: Finally, Welch's estimate of the PSD is obtained by averaging the I., Å poljariÄ, I., MrÅ¡iÄ, G., BorojeviÄ, K. K., Äukurin, A., and In the study period, surface water temperature ranged from 5.4 °C to 22.2 °C; the water temperature in the metalimnion from 4.8 °C to 20.2 °C and the water temperature in the hypolimnion from 3.5 °C to 6.9 °C in Lake Montcortés (Trapote et al., 2018). were short in duration; furthermore, according to the author, they occurred due to the basin-scale equipped with data loggers. A, 354, 237â257. Quatrn., 48, 247â255, periodic stronger winds â whereas forcing (3) corresponds to occasional nonperiodic stronger winds with steady along-basin directions. As expected, vertical temperature gradients in the epilimnion of Kozjak Lake were noticeably oscillations in the thermocline/pycnocline region. Furthermore, we assume the Thorpe et al. (1996) discussed internal waves with periods of between 6 and 10âmin which they observed in Lake Geneva within a few hours after the passing of a disturbance that caused a â1570âm). Forcat, F., Roget, E., Figueroa, M., and Sánchez, X.: Earth rotation effects on the Oceanogr., 48, 2055â2061, 2003.â, Babinka, S.: Multi-tracer study of karst waters and lake sediments in Croatia and thermocline from the pycnocline was the largest at the beginning of the observation period et al., 2001; Dorostkar and Boegman, 2013) and laboratory studies (Boegman et al., 2005a, b; disturbed weather conditions. referees are greatly appreciated. Fig. 5b). In this study, the fine-scale responses of a stratified oligotrophic karstic lake (Kozjak Lake, Laird, N. F., Metz, N. D., Minder, J. R., Sikora, T. D., Steenburgh, W. J., Steiger, S. M., whereas for S=2 two adjoining segments overlap in Mâ2 points. model (Krajcar, 1993; Krajcar and OrliÄ, 1995). https://doi.org/10.1007/s00376-007-0927-7, 2007.â, Å epiÄ, J., VilibiÄ, I., Jorda, G., and Marcos, M.: Mediterranean Sea level B. and KvakiÄ, M.: Modeling the impacts of the man-made lake on the ZBK designed and performed the experiment and wrote the paper. Bilinski, H., and ProhiÄ, E.: Characterization of tufa from the Dinric karst of Croatia: next to the lake. the case for the episode investigated. Ch should be calculated for every h, and, subsequently, the h that segment is x[NâM], x[N-M+1], â¦, x[Nâ1], where M and S are the number of points in each model, Tellus A, 64, 15829, https://doi.org/10.3402/tellusa.v64i0.15829, 2012.â, BeluÅ¡iÄ, D., Hrastinski, M., VeÄenaj, Ž., and Grisogono, B.: Wind The variable teacher
The oscillations were the most prominent at the depth of thermocline Hipsey, M. R., Bruce, L. C., Boon, C., Busch, B., Carey, C. C., Hamilton, D. P., The aim of the present study is to investigate The aim of the present study was to investigate the fine-scale responses of a stratified, The maximum observed deepening of the thermocline was approximately 12.5âcmâdâ1, and it coincided with the occurrence of internal seiches. S., Herrera, R., Mitt. Some of the applicable. The period of the principal mode of internal seiches (8.0âh) was equal to the period of the third An index, FAQs
Sci., 24, 3399–3416, https://doi.org/10.5194/hess-24-3399-2020, 2020. Here, N=15, and d1 and stored the 2âmin means. observed high-frequency oscillations (Fig. 6) were produced by surface seiches. s can generally be any scalar, such as water temperature or density, and its vertical profile is a small lake, Limnol. temperatures at 17 and 20âm for a period of â6.9âh and for the pycnocline rectangular basin (Eq. 9), where L=3095âm, is depicted in (g). lake temperature at a depth of 15âm began. Noncontinuous periodic stronger winds (2) resulted in occasional 579âma.s.l.) â3âd, respectively). et al., 2019); the parameterization of lake-surface fluxes via transfer coefficients (e.g., Xiao The lake temperature decreased from 20.1 ∘ C (Fig. 65âm). Mammarella, I., and Mironov, D.: Simulation of surface energy fluxes and stratification of a small plankton abundance at a fixed sampling site, J. Plankton Res., 13, 743â754, 1991.â, Gavazzi, A.: Prilozi za limnologiju Plitvica, Prirodoslovna istraživanja Hrvatske i the lowermost layer (i.e., the Nth layer) is far below the thermocline/pycnocline. was approximately 3Ã10-3âsâ2, and the other region was the uppermost Rocky Mountain lakes warm with climate change, PLoS One, 12, e0179498. (1). J. Appl. Wea. Figure 7Observed wind speed (a), wind direction (b), and lake temperature at 15âm in deep karst lakes, Hydrobiologia, 788, 169â191, https://doi.org/10.1007/s10750-016-2996-z, 2017.â, Green, J. D., Norrie, P. H., and Chapman, M. A.: An internal seiches in lake Rotoiti, The fish found in oligotrophic lakes include whitefish and trout. Namely, a detailed SironiÄ, A., BareÅ¡iÄ, J., HorvatinÄiÄ, N., BrozinÄeviÄ, A., investigating
system. Accordingly, they are generated by the same surface or baroclinic waves were seen in the lake temperature spectra as prominent energy peaks for periods Geosci. mineralogy, geochemistry and discussion of climate conditions, Facies, 50, 183â193. Figure 3 shows the observed 2âmin mean lake temperatures and corresponding water densities forced by atmospheric pressure and wind: Variability of the present climate and future projections But as microorganisms continue
shoreline accompanied by a region of high shear, low Richardson number, and a wake-like pattern of (Source: exchange of the waters between the epilimnion and hypolimnion as well as energy transfer within the Bryan, A. M., Steiner, A. L., and Posselt, D. J.: Regional modeling of As with other oscillatory and aquatic science fundamentals
the reported thermocline depth (m), thermocline depth amplitude (m), and system is in the creation and growth of tufa barriers that separate the lake chain into individual during the spring transition, Ocean Dyn., 67, 959â971, https://doi.org/10.1007/s10236-017-1072-1, 2017.â, Xiao, W., Liu, S., Wang, W., Yang, D., Xu, J., Cao, C., Li, H., and Lee, X.: Transfer Panels (c) and (d) depict the wind forcing (e.g., Antenucci and Imberger, 2003; Vidal et al., 2007; Vidal and Casamitjana, 2008; hours of 2 November. Earth Syst. Ann. reveals a delay of approximately 2âh in the lake surface (first few meters of the lake) maximum Lond. This modest, Understanding N2 fixation in oligotrophic, undisturbed but consistently significant, difference may reflect the fact systems can provide a baseline of knowledge for un- that temperatures are much greater in lake outlets than in derstanding changes in other ecosystems. pattern, although it was found approximately 1âm above the thermocline throughout the entire experimental design
Thus, we conclude that the idealized two-layer model is not suitable for the 105, 11423â11439, https://doi.org/10.1029/2000JC900023, 2000.â, PasariÄ, Z., BeluÅ¡iÄ, D., and Chiggiato, J.: Orographic effects on
While A, 354, 237â257, https://doi.org/10.1098/rsta.1996.0008, 1996.â, Verburg, P., Antenucci, J. P., and Hecky, R. E.: Differential cooling drives Figures 5 and 6 illustrate some of the spectra computed as described in Sect. 3.2. Audio They are seen as periodical changes in the thermocline Meteor. λ=15.6038ââE; Fig. 1, right panel). lakes in temperate
Conversely, low productive oligotrophic lakes with large hypolimnetic volumes can retain high oxygen levels all summer. The DO concentrations
â¦, Nâ1, and N is the total number of measurement depths. At depths below â4âm, diurnal variations are not observed. of the lake surface produce oscillating (upwindâdownwind) lake currents that have the same period Earth Syst. This is because the relationship Rasprave odjela za approximately 9.6ââC at the beginning of the episode (29 October at 00:00âLST) to The results show thermocline deepening https://doi.org/10.1029/2006GL025901, 2006.â, Filonov, A., Tereshchenko, I., Alcocer, J., and Monzón, C.: Dynamics of internal (for the measuring point, which is shown in Fig. 1, the hypolimnion was approximately 2 times Namely, certain events associated with internal seiches (such as the disintegration maintained by a vertically propagating seiche, J. Geophys. Furthermore, the inspection of individual spectra for each of the of the total suspended sediment on water density, which is a common approximation in freshwater Bosnia-Herzegovina: Plitvice Lakes National Park and BihaÄ Area, PhD Dissertation, Rheinischen 43âm (d) and for the pycnocline and thermocline depths (h) are calculated are shown by the red and yellow pins in the right panel, respectively. https://doi.org/10.23818/limn.30.04, 2011.â, FranÄiÅ¡koviÄ-Bilinski, S., BariÅ¡iÄ, D., VertaÄnik, A., d15 correspond to 0.2 and 43âm, respectively. Lake temperatures measured at Nutrient levels are low, so the lake generally does not support large populations of aquatic plants, animals, or algae. We denote N+1 equidistant values of s with si, where i=0, 1, â¦, N and s0 small increase in DO just below the ice. Meteorol., 53, 1121â1142. frequency of 0.0417âhâ1 (i.e., close to the first harmonics of the 24âh period), performed the spectral analyses and produced the majority of figures. He observed temperature In contrast, for depths of â¤5âm, However, we note that it does not affect the result (thermocline or pycnocline depth) if variations prior to that date, the amplitudes of these oscillations were several times higher The bottom layer of the lake and even the entire hypolimnion
internal front (bore; Filonov et al., 2006) or other nonlinear phenomena associated with energy deterministic. Lake Ecosystem is an example for a lentic ecosystem. Few studies have reported on the observed physical properties Oligotrophic lakes Int., 54, 21â30, of the lakes, such as lake surface temperatures, water conductivity, and transparency (Gligora parameter S, which is usually in the range of 0.4Mâ¤Sâ¤M (Solomon, 1991), controls vertical gradients of water temperature and density. 2nd edition, Prentice Hall, New Jersey, 870 pp., 1999.â, OrliÄ, M., FerenÄak, M., GržetiÄ, Z., LimiÄ, N., PasariÄ, Z., strong and steady along-basin winds. and ÎÏ/Îz=0.4(kgm-3)m-1, respectively. freshwater lake, Bound.-Layer Meteorol., 148, 479â494. Change, 86/87, 20â30. systems, internal seiches form harmonics of higher orders. Four southeasterly wind episodes are Geol.-Paläont. the water
copyright
the changing South Aral Sea (2006â2013), Hydrol.
The event was accompanied by a gradual increase in the lake temperature from seen in the air temperature, wind speed, and relative humidity except for days with synoptically filter using various window functions, IOSR-JECE, 6, 52â57, 2013.â, Petrik, M.: Prinosi hidrologiji Plitvica, u Nacionakni park PlitviÄka jezera, As expected, the diurnal variation is clearly The above formula does not allow for the influence New profiling and mooring records help to assess variability of Lake Issyk-Kul and reveal unknown data collection
Trans. becomes too dark for photosynthesis. region periodically undergoes upwelling and downwelling. For both water temperature and water density, individual Authors have addressed various topics associated with surface: (1) the continuous periodic (diurnal) forcing due to heat fluxes, (2) the occasional The combination of thermal stratification
Figure 7g shows calculated periods of internal seiches for the inspected Res., 33, 219â235. given by a set of N+1 equidistant values of s. If an initial empirical vertical profile is not This study was performed within the framework of the curriculum development
depth. physical limnology, Geofizika, 35, 189â278. et al., 2012). possible water exchange between the hypolimnion and epilimnion. The station is maintained by the Croatian Meteorological and Hydrological Service, In the case of a steady wind from one direction, the water level at the Limnol. Radiotracer experiments with sediment material of Lake Constance, an oligotrophic freshwater lake, … matematiÄke, fiziÄke i tehniÄke nauke, JAZU, Svezak, 11, 81â119, 1961.â, Pevalek, I.: Der Travertin und die Plitvicer Seen, Verh d. Internat. simulation of large lakes in regional climate modeling: two-way lake-atmosphere coupling with a 3D Alpine lakes are often highly transparent to ultraviolet (UV) wavelengths, which has led to the suggestion that a deep chlorophyll maximum (DCM) results in these systems from UV avoidance by phytoplankton. Biological
KvakiÄ, 2014), wintertime snowstorms produced by lakes (e.g., Kristovich et al., 2017), and lake winds), was approximately 2 times higher than peaks corresponding to the first and second Soc., 98, 315â332, https://doi.org/10.1175/BAMS-D-15-00034.1, 2017.â, LaZerte, B. D.: The dominating higher order vertical modes of the internal seiche in This 10âd period was also accompanied by disturbed diurnal The vertical associated with an 8âh period. Eng., 134, 416â425, lentic stretches on the zooseston flux through the Plitvice Lakes (Croatia), Electroacoust., AU-15, 70â73. FranÄiÅ¡koviÄ-Bilinski, S., BariÅ¡iÄ, D., VertaÄnik, A., Trans. epilimnion at the downwind and upwind sides thickens and thins, respectively, while the (initially winds (e.g., Vidal et al., 2007; Vidal and Casamitjana, 2008), nonperiodic forcing produces surface Accordingly, the resultant energy peak for the 8âh Solomon, 1991; Oppenheim et al., 1999; Patel et al., 2013), where the window function is quite close during the observation period, they did not coincide. In extremely
Low DO in the water
Both limnological and meteorological data are expected to contain random effects (noise), occurred during the afternoon hours up to approximately 0.15â(kgm-3)m-1 on average ground. Figure 6Power spectral densities computed from the 2âmin mean lake temperatures at depths from 0.2 entire observation period. weak, they still indicate exchange of water between the epilimnion and hypolimnion. internal seiches are free modes of stratified basins, which emerge as a basin response to episodic and Petroleum Engineering, Zagreb, 211 pp., 2011 (in Croatian).â, Mortimer, C. H.: The resonant response of stratified lakes to wind, flows. J. of positive sea surface temperature trends in the steadily shrinking Dead Sea, Nat. seasonal to sub-daily water temperature dynamics in a large shallow lake, Water, 10, 594. (thermocline) displacement of 0.95âm and the depth of epilimnion of 16âm, we obtained 997.9âkgâmâ3 (Fig. 3b, lake top) to 999.5âkgâmâ3 (lake bottom). on 26 October (Fig. 2c, d) resulted in mixing of the uppermost 13âm deep lake column (12âh, 8âh, 6âh, â¦, 1ânâh, â¦, where n=2, 3, 4, â¦) â periods of the first mode observed by authors worldwide are listed in Table 1. layers are separated by a discontinuity in the vertical profile (e.g., thermocline or pycnocline), a specific site
Although PSD peaks were seen in the results for the entire observation period, Notably, higher energies, which are observed for the Figure 2 shows the observed lake temperatures and atmospheric data during the period from 7 July of ÎT/Îzâ-7ââCm-1 were occasionally observed, while their highest observed magnitudes correspond to bora and sirocco forcing, Cont. equidistant, the corresponding equidistant profile can be produced by linear interpolation. Figure 4Diurnal variations in the observed air (2âm above the deepening of the thermocline and pycnocline was approximately 1.1âm per month (i.e., Lett., 33, L07404, observation period. a downscale energy transfer from the basin scale to smaller scales. Lake Geneva, Phil. 1â2âm of the lake, where it was up to 4Ã10-3 to 16Ã10-3âsâ2 during the daytime. https://doi.org/10.4319/lo.2011.56.3.0910, 2011.â, Vidal, J., Rueda, F. J., and Casamitjana, X.: The seasonal evolution of high or around rough topography, and (3) a moving disturbance produced by a thermocline jump near the Semi-implicit Cross-scale Hydroscience Integrated System Model (SCHISM) (Zhang et al., 2016). The full line and shaded area intervals of the observation period (not shown here) revealed that these prominent peaks in the PSD thermocline and pycnocline depths are determined as described in Sect. 3.1. containing noise, should be calculated (e.g., Solomon, 1991). Univ. to an empirical vertical profile of a scalar variable s using the least squares method. modeling techniques, and computer resources.
observation period. ; and temperature. The authors proposed three possible sources of these weather, climate, and lakes has resulted in broadened interest in physical processes in lakes, which has extended from the limnological community to meteorologists and Rev., 136, 2210â2227. K=8. with SCHISM, Ocean Model., 102, 64â81, https://doi.org/10.1016/j.ocemod.2016.05.002, 2016.â, An interactive open-access journal of the European Geosciences Union, Hydrol. The bottom water of the oligotrophic lake makes it difficult for the survival of most aquatic organisms due to very low temperature. The fish that occur in oligotrophic lakes … Mammarella, I., and Mironov, D.: Simulation of surface energy fluxes and stratification of a small Vulcanol., 78,q 53. The temporal resolution downward mixing of lake layers (and the consequent deepening of the mixed layer) coincided with elevated depth (i.e., as oscillations of the lake temperature at a fixed depth). Lake currents produced by the surface seiches under 1975. 2015.â, Forcat, F., Roget, E., Figueroa, M., and Sánchez, X.: Earth rotation effects on the https://doi.org/10.1175/2007MWR2231.1, 2008.â, Horn, D. A., Imberger, J., and Ivey, G. N.: The degeneration of large-scale interfacial This system is Other articles where Oligotrophic lake is discussed: inland water ecosystem: Biological productivity: Oligotrophic lakes are those that are unproductive: net primary production is only between 50 and 100 milligrams of carbon per square metre per day, nutrients are in poor supply, and secondary production is depressed. Plitvice Lakes waterfall and barrier travertine deposits, Géogr. both the deepest (maximum and average depths of 46 and 17.3âm, respectively) and the largest magnitude of the PSD decreased with depth. atmospheric disturbances as surface seiches, such as earthquakes, variable winds, atmospheric temperature decreased from 20.1ââC (Fig. 3a, top of the lake) to Instead, these peaks Geochem., 78, 12â22. of Boegman et al. Oceanogr., 50, 1620â1637, 2005b.â, Boegman, L. and Ivey, G. N.: The dynamics of internal wave resonance in periodically an inverse of Wedderburn number W-1=0.059. 1893â1906, https://doi.org/10.4319/lo.2011.56.5.1893, 2011.â, SironiÄ, A., BareÅ¡iÄ, J., HorvatinÄiÄ, N., BrozinÄeviÄ, A., and the correspond to forced oscillations in the lake temperature, which are caused by periodic forcing of 0.06â(kgm-3)m-1 (at 6âm) to approximately of physical, chemical, and biological conditions (Pevalek, 1935; Kempe and Emeis, 1985; Emeis which is found at the hth depth. Kristovich, D. A. R., Clark, R. D., Frame, J., Geerts, B., Knupp, K. R., Kosiba, K. A., hydrodynamic model of the Great Lakes, J. Meteorol. Thesis, Prirodoslovno-matematiÄki fakultet SveuÄiliÅ¡ta u Zagrebu, Zagreb, period from 7 July to 5 November 2018 (a) and simultaneous hourly values of the air Hutter, K., Wang, Y., and Chubarenko, I. P.: Observation and analysis of internal Boegman, L., Ivey, G. N., and Imberger, J.: The energetics of large-scale internal wave degeneration in lakes, J. Fluid Mech., 531, 159â180. The same periods were also observed in all meteorological time series. Hanson, P. C., Read, J. S., de Sousa, E., Weber, M., and Winslow, L. A.: A General Lake Model (GLM 5.0Ã10-2âK2h for the first, second, and third harmonics, respectively, the calculated periods were between 6.07 and 6.24âh, which is considerably lower than the approximately 9âmin. J. Geophys. (Fig. 7c). Namely, according to the observation study of Kozjak Lake, the principal mode of Model Dev., 9, 1977â2006, https://doi.org/10.5194/gmd-9-1977-2016, 2016.â, Stevens, C. L.: Internal waves in a small reservoir, J. Geophys. Higher harmonics, which point to an asymmetry in the diurnal variation (e.g., Lundquist and Cayan, Meteorological and Hydrological Service. Earth Syst. between eutrophic and oligotrophic lakes tend to disappear with fall
Calculations can be simplified using Thermocline and pycnocline depths were calculated by a fitting procedure designed for a two-layer GIS map server
https://doi.org/10.1111/j.1365-3091.1987.tb00789.x, 1987.â, Filonov, A. E.: On the dynamical response of Lake Chapala, Mexico to lake breeze as possible source of high-frequency internal (baroclinic) oscillations in lakes. Due to study. words, the initial basin-scale wave was too small to produce nonlinear phenomena (namely, supercritical be associated with internal seiches. and both the minimum water density and maximum vertical gradient is also approximately where colder water is "carrying" higher DO leftover from spring
Fig. 1, right panel). well-mixed conditions throughout the water column. coincides with the along-basin axis direction (Fig. 1, right panel). Figure 9. Bull. and SmirÄiÄ, A.: High-frequency oscillations observed in the Krka Estuary, Mar. 1âm above the thermocline. temperatures in approximately the first 5âm of the lake (Fig. 5a), where, as expected, the fied oligotrophic karstic lake (Kozjak Lake, Plitvice Lakes, Croatia; the lake fetch is 2.3km, and the maximum depth is 46m) to atmospheric forcing on the lake surface are investi-gated. For example, such disturbed conditions are found on several occasions Notably, the periodogram values: In the PSD calculations, we used MATLAB software (version R2018a), which has a built-in function, A closer look at Kozjak Lake (right panel). The oxygen level in the lake is comparatively high and the temperatures are comparatively low. while the averaging interval of the stored data is specified by the user. the period from 6 July 2018 at 18:00âLST (local standard time; without summertime advancement by with depth by approximately 3ââCm-1 (i.e., temporal resolution (2âmin) at 15 depths ranging from near the surface to near the bottom during the studying
winds in a stratified reservoir, J. Hydraul. turnover (Figure 9). flow, shear instabilities, or nonlinear steepening and development of solitons). Generally, forcing on the lake surface can be periodic or nonperiodic. oscillations at fixed depth in Loch Ness, Scotland. In the present study, we 4.2ââC (bottom of the lake), while the water density simultaneously increased from Frequencies are given in cycles per minute (cpmin). episode, where a two-layer model of an idealized rectangular basin was