Evaporation from Lake Kasumigaura : annual totals and variability in time and space

Evaporation E from Lake Kasumigaura, the second largest lake in Japan, was estimated continuously at a 3-h interval for the period of 2008–2012 by means of a bulk formulation applied to 23,468 grids covering the whole lake surface. A functional form of the bulk coefficient was determined from eddy correlation measurements at the central part of the lake. Wind speed (U), temperature, humidity, and infrared radiation surface temperature, from which the specific humidity qs of the water surface was determined, were also measured. Specific humidity q and U at 10 m above the surface of each grid were derived from routine measurements at meteorological stations in and around the lake, by applying the Kriging interpolation scheme. This operation produced not only the totals but also the horizontal variation in E. The mean annual E was estimated as 911 (± 42) mm, which is within the range of previous estimates of 671–1003 mm/yr. Seasonally, E followed the change in net radiation with a short (< 1 month) phase delay caused by stored energy in the water body. Year-to-year variation was small. Horizontally E tended to be larger in the central and southern parts of the lake, reflecting stronger wind regime there.


INTRODUCTION
Lake Kasumigaura is the second largest lake in Japan with a surface area of 220 km 2 , mean depth of 4 m, and mean storage of 8.6 Mm 3 .Being located in the Greater Tokyo Region, Lake Kasumigaura serves as a vital source of water resources (see e.g., NILM-MLIT, 2003), with their accurate estimation important for the planning sector and policy makers.For this estimation, information on evaporation E is generally required.However, in many cases, E is the least available information among the hydrologic elements due to technical difficulties in its measurement and estimation.For Lake Kasumigaura, several estimates of evaporation are available in the literature.Sudo and Arakawa (1977) applied Penman's equation (see, e.g., Brutsaert, 2005) to water tem-peratures measured along the northeastern shore of the lake and to meteorological data from Tateno Observatory (36.055°N, 140.125°E; some 25 km west of the center of the lake) of the Japan Meteorological Agency (JMA).They obtained monthly estimates of E with an annual total of 1003.2 mm/yr for 1973.Tsuchiya et al. (1981) made use of measurements of pan evaporation at two locations along the northern and southern shores, with an annual lake evaporation E of 671 mm/yr estimated for 1979 with a pan coefficient of 0.8.Kondo (1994; for the details of method, see also Kondo and Kuwagata, 1992) derived monthly values E for Lake Kasumigaura by solving an energy balance equation by iteration together with bulk transfer equations for sensible and latent heat fluxes, as well as a heat conduction equation, for the flux to/from the lake water body, which was assumed to be well-mixed and in an isothermal condition with a depth of 3 m.Meteorological data was likely for 1961-1964 and from the JMA Mito Observatory (36.380°N, 140.467°E; approximately 40 km N of the center of the lake) (Kondo, 2008, personal communication) .Annual E was estimated to be 844 mm/yr.Thus the difference among the previous estimates of annual E is quite large, with the difference between the largest and smallest estimates (= 332 mm) as large as 37% of the overall mean (= 893 mm) of the three estimates.Recent advances in measurement technology should allow direct and more accurate determination of lake evaporation; however, except for one short-term early study (Mitsuta et al., 1970), no direct measurements have been reported so far.This is probably due to the difficulty in finding proper measurement platforms over lake surfaces.Thus the purpose of this study was to revisit the issue of evaporation of Lake Kasumigaura, and to derive more accurate E estimates based on direct and long-term measurements using an observatory (see below) located at the center of the lake.To achieve this goal, not only the directly-measured evaporation, which represents a relatively small area on the scale of 10 4 m 2 , but also a spatial distribution and average of E over the entire lake surfaces were determined based on grid application of bulk formulation.

Study area and measurements
Sotonasakaura (6 km 2 ), and connecting rivers (Figure 1).The altitude of the lake is close to sea level and the surrounding area is relatively flat with an altitude of 20-30 m.In fact, the outlet of the lake is only 15 km from the Pacific Ocean, connected through the Tone river.Some 30 km to the northwest is Mt Tsukuba (877 m) which constitutes the headwater of the Kasumigaura watershed.
Data used in the analysis were obtained at several locations (Figure 1).For the direct measurement of evaporation, an eddy correlation system with a sonic anemometer (Gill, R3A) and an open-path gas analyzed (Li-Cor, LI7500) have been installed at the Koshin Observatory of the Kasumigaura River Office (hereafter referred to as KRO, Kanto Regional Development Bureau, Ministry of Land, Infrastructure, Transport and Tourism of Japan) located at the center (36°02′35′′N, 140°24′42′′E) of Lake Kasumigaura.The minimum fetch of the observatory is 3 km in the northeasterly direction, while it is 4-17 km in the other directions.Turbulence data were subjected to the common quality control procedure (e.g., Lee et al., 2004) with details of the measurements and analysis as described in Wei et al. (2014).
Wind speed, humidity and temperature routinely measured by KRO, Lake Kasumigaura Water Research Station (WRS) of the National Institute for Environmental Studies, JMA, Ibaraki Prefecture (IB), and Hyakuri Air Base (HAB) of the Japan Air Self-Defence Force (see Figure 1 for locations) were also used to derive grid values to be input into the bulk equation as described below.Note, however, the data from IB and HAB were only available for 2008.Prior to this operation, wind speeds measured at each station at a certain height were converted to 10 U , wind speed at 10 m, by applying the profile equation under neutral conditions with roughness length determined for each station by applying the method of Kondo and Yamazawa (1986).This determines the weighted mean of roughness lengths assigned to land use type, with weighing factors being the fraction of each land use cover in the upwind area.Land-use fraction was determined by analyzing GIS data of the Lake Kasumigaura watershed (GSI, 2005).Details of this analysis are explained in Ikura (2010).For humidity data, the height conversion was not applied since this would require surface evaporative fluxes at each meteorological station, which are usually not available; also sensitivity analysis has shown that conversion does not produce markedly different results (Ikura, 2010).

Bulk equation to estimate evaporation
The high-quality E fluxes derived by the eddy correlation method were combined with wind speed, relative humidity and temperature measurements from the Kohsin Observatory to derive the neutral bulk coefficient C EN as a function of wind speed as, where b 1 = 0.000908, b 2 = 0.217, b 3 = 0.00114, and b 4 = -1.54× 10 −5 (Wei et al., 2014).10N U represents the wind speed at 10 m under neutral conditions and was derived by converting actual measurements of 10 U , which may not nec- essarily be obtained under neutral conditions, by applying the profile equation and stability correction function (e.g., Burtsaert, 2005).Although the exact functional form of the bulk coefficient is open to discussion in view of uncertainties in the scalar transport mechanism and ambiguity of the definition of bulk coefficient (Wei et al., 2014), Equation (1), should work satisfactory for the present purpose of reproducing E measured by the eddy correlation method, since it is a locally calibrated equation.In the estimation mode, E was determined by applying the bulk equation, where q and q s are respectively the specific humidity at the reference height (10 m), and at water surface, and the overbar represents the temporal averages.C E = C EN and 10 10N U U  were assumed and Equation (1) was employed in Equation (2).This is essentially unavoidable as the incorporation of the stability effects through the iteration scheme in the calculation of each grid would be time consuming and quite complicated.However, the impact of these assumptions is not large, as the bulk coefficient is a very weak function of the atmospheric stability.Indeed, E values from the eddy correlation method compared well (rms error = 0.03 mm/h) with those from Equations ( 1)-( 2) by means of the Koshin observatory.
To determine the evaporation distribution over the surface of Lake Kasumigaura, Equations ( 1)-( 2) were applied to each grid covering the lake at 3-h intervals for the five years of 2008-2012.For this calculation, input data of 10 U , q and q s at each grid were required.10 U and q were determined by applying Kriging method to the station data (see above), Figure 1.A map showing Lake Kasumigaura and its surroundings.Circles denote stations that measure only the wind speed (black symbols indicating those operated by JMA, red symbols by KRO, and green symbols with a center dot by IB and HAB).Squares denote those that measure wind speed, temperature and humidity (with same symbols notation as wind speed, and white symbols the WRS station).Contour lines of the altitude of the land areas and annual evaporation (mm/yr) in Lake Kasumigaura in year 2012 (see the result section of the main text) are also shown.Blue lines are major rivers and canals while q s was assumed to be the same everywhere in the Lake.Thus measurements by an infrared radiation thermometer (Everest Intersci., 4000) made at the Koshin Observatory were used to derive q s values.This was acceptable as the surface temperature difference of the lake water was quite small, as shown by Ikura (2010) who analyzed satellite infrared images on 32 clear days and determined the surface temperature distribution in Lake Kasumigaura.The mean value of the standard deviation of the surface temperature of each lake image at around 10 am was as small as 1.0°C.This small difference probably reflects the fact that water is almost always well mixed as confirmed by the vertical temperature profiles data of KRO.Note also that the advected energy by river discharges during heavy storm runoff events could influence the distribution of lake water temperature.However, time series analysis of temperature of inflow river and the lake, river discharge and rainfall indicated that lake water temperature did not show any clear responses to the storm events (not shown), and thus such influence can probably be ignored in the present analysis.
For the application of the Kriging method to the study area, a rectangular area that includes Lake Kasumigaura was created and divided into 521 × 334 grids (with a grid size of approximately 90 × 90 m) and the specific humidity and wind speed of each grid at 10 m above the surface were derived.The number of grids covering the lake surface was 23,468.In this application, the development of an internal boundary layer (IBL) at the land-water interface was ignored, which could potentially lead to an error in estimation of evaporation near the downwind region of the interface.For example, when drier air comes onto the lake from surrounding land surfaces, an IBL develops on the water surface.What determines the rate of evaporation of the lake is the humidity vertical gradient within this IBL.Near the shore line where IBL development has just commenced, the IBL depth could be less than 10 m.Evaporation could then be overestimated in this case because the humidity at 10 m is drier (as it reflects conditions of the land surface) than that within the IBL (which reflects the water surface), resulting in a larger vertical humidity gradient.However, a comparison of the specific humidity q above lake water surfaces and that above land surfaces has shown that they are not very different (even though the former is somewhat larger), and that the small difference between the two is much smaller than the difference between the specific humidity q s of the lake surface water and that of the air.Thus in the case of Lake Kasumigaura, IBL development can be ignored without causing a large error in the estimation of E. Nevertheless it should be kept in mind that the present method could potentially introduce error in E estimation near the downwind part of shore lines.

RESULTS AND DISCUSSION
Figure 2 shows monthly evaporation averaged over Lake Kasumigaura derived by calculating means for all grids over the lake surface.The figure also shows the measurements at the Koshin observatory, including E values by the eddy correlation method, supplemented by the bulk equation, Equation ( 2) when sensors outputs were judged not reliable (for example under rainy conditions), temperature T a , and wind speed U. Energy balance components of net radiation R n , sensible heat flux H, latent heat flux L e E (in which L e represents the latent heat for vaporization), the difference between net radiation and heat fluxes going into the water body R n -S (= H + L e E) measured at Koshin are also indicated.Average E of the Lake and E at the Koshin observatory were in general in good agreement, although the Koshin E tended to be somewhat larger than the horizontal averages.When the annual total was compared, the mean evaporation over the lake was E = 911 (± 42) mm/yr, while E at the Koshin observatory was 948 (± 24) mm/yr.Year-to-year variation was thus not very large.
It is clear that the seasonal change in E is essentially driven by the input energy (R n ), as the peak of evaporation appears in the summer season of July-August and minimum values in winter (December to February).However, a match of the two curves is not exact since a short (< 1 month) phase delay, as well as the shape deformation, are evident.This is caused by the heat flux S going into and coming out of the lake water body.When the R n -S curve, i.e., the available energy, is compared with the E curve, their similarity is quite clear.Thus, the stored energy acts to slightly modify the seasonal change in E primarily determined by the input energy R n .This can also be confirmed by comparing average E of the Lake and E at the Koshin observatory.Particularly in the fall-winter season, E at Koshin is larger than the average.This is because Koshin is located at the deepest (about 7 m) area in the lake and the larger stored energy S during summer is released to enhance evaporation.The influence of U on the seasonal change in E appears to be smaller than that of the available energy.
The horizontal distribution of annual evaporation in 2012 is also shown in Figure 1.The other four years showed essentially the same distribution and so are not shown.Evaporation tended to be higher at center of the lake and towards the south.Unlike the case of seasonal variation, this is not because R n was larger in this area; it was more or less uniform.Rather, it is mainly because wind speed in this area tends to be stronger from the center of the lake to the south due to extended open flat topography (Figure 1; see also the discussion in Ikura, 2010).Thus the next important factor controlling E, i.e., wind speed becomes relevant.
The accuracy of the E values derived by means of the bulk equation can be assessed by comparing E values at the grid where the Koshin observatory is located and those determined by the eddy correlation method.As mentioned before, the rms error is 0.03 mm/h for hourly estimates.For the monthly totals, it is 17.3 mm, and for annual values, it is 123.3 mm (14% of the mean annual E).This reflects mainly the uncertainty in the bulk coefficients, assumptions employed in the analysis, and observational errors (including eddy correlation method).
Comparison of the derived evaporation from Lake Kasumigaura can be made with previous estimates.For this purpose, average values for the annual total and monthly evaporation over five years are more appropriate since the target periods are different among the reported values.Thus E = 911 mm/yr from the present study was compared with previous estimates, and it is immediately clear that this value falls within the range of previous estimates (671-1003 mm/ yr) but is somewhat larger.A monthly comparison is shown in Figure 3. Larger summer E may be one reason for the larger annual total of the present study.There are at least three possible reasons for the difference among the results: (i) differences in methodology employed by each study, (ii) use of meteorological data observed over land surfaces rather than lake surfaces in the previous studies, and (iii) differences in climate between the target years.For (ii), differences in the annual averages for 2008-2012 between Tateno and Koshin are as follows: air temperature T a (+ 0.4°C), relative humidity RH (+ 8%), wind speed U (+ 2.6 m/s), and solar radiation R sd (1.3 W/m 2 ).A positive sign means higher values at Koshin.Similarly between Mito and Koshin, the differences were T a (+ 0.7°C), RH (+ 8.8%), U (+ 2.7 m/s), and R sd (not available).For (iii) the differences between 1973 and the 2008-12 period were T a (+ 1.2°C), RH (-1.7%),U (+ 0.02 m/s), and R sd (0.6 W/m 2 ) at Tateno.A positive sign indicates an increase in that value compared to the past.At Mito, they were T a (+ 0.7°C), RH (-4.0%),U (-0.5 m/s), and R sd (not available) between the 1961-64 period and the 2008-12 period.Thus except for temperature, the difference in location seems more important in causing differences in the meteorological data.In particular, wind speed difference was the largest, and this appears to be the reason for the larger estimates in the present study, particularly compared to Kondo (1994).In addition, in the case of the Penman estimate used by Sudo and Arakawa (1977), the difference in methodology appears to be important, i.e., (i).A common application of Penman's equation involves a so-called wind function optimized for grass surfaces.When this is replaced by a theoretical function for water surface (e.g., see Equation (10.18) of Brutsaert, 1982)  It is more difficult to interpret the differences in pan estimation, but if we take a mean trend in pan evaporation reported for Japan by Asanuma et al. (2004), 2-4% per decade over the period of 1967-2000, E = 671 mm/yr of Tsuchiya et al. (1981) can be converted to 595 mm/yr in 2008-2012 (with a trend of 3% per decade and the mean pan evaporation of 812 mm/yr for 1977-1979(Tsuchiya et al., 1981))).Thus the difference becomes even larger.Note, however, Tsuchiya et al. (1981) suspected underestimation of pan-based E estimates; they made an experimental investigation but they were not conclusive.

CONCLUSIONS
The evaporation distribution over a lake water surface was determined over Lake Kasumigaura continuously at a 3-h interval for 5 years by means of grid-based application of a bulk equation.In this approach, the lake surface was divided into a small grid (90 by 90 m), and wind speed and specific humidity of each grid were estimated by applying the Kriging method to meteorological data measured at stations in and around Lake Kasumigaura.A grid value of bulk coefficients was determined from wind speed by applying Equation (1) derived from eddy correlation observations at the Koshin observatory at the center of Lake Kasumugaura.These were used in the bulk equation, Equation (2), applied to each grid to determine evaporation.
Results were averaged over time and over lake surfaces; the mean annual evaporation was determined for five years as 911 (± 42) mm, which is larger than, but within the range of, previous estimates.The main reason for the difference was identified as the use of wind speeds measured over lake surfaces in the present study, which tend to be higher than that over land as used in previous estimates.Another factor is the use of a wind function for grass surfaces in the case of Penman's equation.
Horizontally, evaporation was larger at the center of the Lake and to the south, due to the strong wind regime in this part of the lake.The lake evaporation followed seasonal net radiation with a small phase delay.This delay was caused by energy flux going into and coming out of lake water heat storage.Year-to-year variation was not very large during the five year period of 2008-2012.

Figure 2 .
Figure 2. Seasonal changes in monthly evaporation averaged over Lake Kasumigaura (shaded figure with annual sums indicated).Also shown are monthly mean values of evaporation E, wind speed U, air temperature T a , net radiation R n , sensible heat flux H, and sum of R n and heat flux S going into the water body, all measured at the Koshin Observatory Figure 3.Comparison of monthly evaporation reported in previous studies to the present study.Present result are based on 5-year values with mean and standard deviation presented for each month