Lake Heat Storage Research Articles

Characterizing Spatial Heterogeneity in Reservoir Evaporation within the Rio Grande Basin Using a Coupled Version of the Weather, Research, and Forecasting Model

Abstract Increasing evaporative demand from storage reservoirs is aggravating water scarcity issues across the American West. In the Rio Grande basin, open water evaporation estimates represent approximately one-fifth of all water losses from the basin. However, most estimates of reservoir evaporation rely on outdated methods, point measurements, or simplistic models. Warming temperatures and increasing atmospheric evaporative demand are stressing overallocated resources, increasing the need for improved evaporation estimates. In response to this need, we develop open water evaporation estimates at Elephant Butte Reservoir (EBR), New Mexico, using three evaporation models and field measurements. Few studies quantify spatial heterogeneity in evaporation rates across large reservoirs; we therefore focus our efforts on using the Weather Research and Forecasting Model coupled to an energy budget lake model, WRF-Lake, to simulate evaporation across EBR over the course of two years. We compare results from WRF-Lake, which simulates lake heat storage, to results from the Complementary Relationship Lake Evaporation (CRLE) model and the Global Lake Evaporation Volume dataset (GLEV). Results indicate that monthly and annual evaporation totals from WRF-Lake and GLEV are similar, while CRLE overestimates annual evaporation totals, with monthly peak evaporation offset compared to WRF-Lake and GLEV. While WRF-Lake and GLEV appear to capture monthly and annual evaporation totals, only WRF-Lake simulates differences in evaporation totals across the reservoir surface. Average annual evaporation at EBR was approximately 1487 mm, yet annual totals differed by up to 545 mm depending on location. This study improves understanding of open water evaporation and elucidates limitations of extrapolating point in situ or bulk evaporation estimates across large reservoirs. Significance Statement Changes in climate are amplifying the loss of stored water in reservoirs due to increases in evaporation. Water managers need to account for this water loss, but many current methods do not accurately reflect the temporal and spatial variability in evaporation across large, heterogeneous reservoirs. To address this gap, we use a numerical weather prediction model coupled to a lake model to simulate spatial heterogeneity in reservoir evaporation on a subdaily time step. Our results suggest that bulk evaporation models may be sufficient for estimating evaporation at smaller, more homogeneous reservoirs, but more complex formulations may be more appropriate for estimating evaporation rates at large, complex reservoirs and for better understanding the heat storage affects that influence temporal variability of evaporation.

A Quantification of Heat Storage Change-Based Evaporation Behavior in Middle–Large-Sized Lakes in the Inland of the Tibetan Plateau and Their Temporal and Spatial Variations

A large number of different-sized lakes exist in the inland area of the Tibetan Plateau (TP), which are examples of the important connection between the atmosphere and hydrosphere through the analysis of lake surface convergence and evaporation processes. The evaporation level changes that occur in middle–large-sized lakes (surface area > 50 km2) in the area directly influence the regional mass and energy balance values, atmospheric boundary layer heat and humidity structures, and weather processes occurring in the lower-reach areas. The studies conducted in the literature at present, concerning lake evaporation processes, generally overlook the differences in lake heat storage behavior due to the reduced amount of data in the literature concerning lake bathymetry. According to the in situ bathymetric data obtained for 68 middle–large-sized lakes in the inner basin of the TP, in this study, we calculated their heat storage (G) change values by using the different vertical-depth water-temperature-change integral method, and we established a regression equation for the heat storage and lake surface net radiation values for 68 lakes. The evaporation rates of 134 middle–large-sized lakes larger than 50 km2 in the inland are of the TP were calculated by obtaining the G regression result and adopting it into the Penman model, as well as estimating the evaporation losses of theses 134 lakes from 2002 to 2018. The result shows that the annual average evaporation rate for these lakes is 927.39 mm/year, with an insignificant upward trend (0.10 mm/year). This method achieved good accuracy compared with the Bowen ratio method, which estimates the evaporation rate during the ice-free season, with a high correlation coefficient (R) value of 0.95 and least root mean square error (RMSE) value of 61 mm. The annual mean evaporation rate can be divided into the southern and northern lake groups along a 34°N line with a difference of 314.41 mm/year. The annual average evaporation volume of these lakes was 25.02 km3 and showed an upward trend of 0.35 km3/year. Among them, the annual average evaporation volume contribution ratio of level-1 lakes (50 km2 ≤ lake’s area < 100 km2, 61 lakes) was 14.04%, showing an upward trend, and the contribution of level-3 lakes (lake’s area ≥ 500 km2, 10 lakes) was 41.50%, showing a downward trend. There were no obvious changes in the level-2 lakes (100 km2 ≤ lake’s area < 500 km2, 63 lakes), which maintained at the same level in approximately 44.46%. Air temperature is the most important factor affecting the evaporation rate of lakes, while the lake surface area is the main factor affecting lake evaporation volume. Our study, considering the actual lake heat storage value, provides a useful reference for further improving lake water budget balance values and watershed hydrologic features in the inland closed lakes located in the TP.

Contrasting hydrological and thermal intensities determine seasonal lake-level variations – a case study at Paiku Co on the southern Tibetan Plateau

Abstract. Evaporation from hydrologically closed lakes is one of the largest components of the lake water budget; however, its effects on seasonal lake-level variations remain unclear on the Tibetan Plateau (TP) due to a lack of comprehensive observations. In this study, weekly lake evaporation and its effects on seasonal lake-level variations are investigated at Paiku Co on the southern TP using in situ observations of thermal structure and hydrometeorology (2015–2018). Lake evaporation from Paiku Co was estimated to be 975±142 mm during the ice-free period (May to December), characterized by low values of 1.7 ± 0.6 mm d−1 during the pre-monsoon season (May to June), high values of 5.5±0.6 mm d−1 during the post-monsoon season (October to December), and intermediate values of 4.0±0.6 mm d−1 during the monsoon season (July to September). There was a ∼ 5-month lag between the maximum net radiation (June) and maximum lake evaporation (November). These results indicate that the seasonal pattern of lake evaporation from Paiku Co was significantly affected by the large lake heat storage. Contrasting hydrological and thermal intensities may play an important role in the large amplitude of seasonal lake-level variations at deep lakes like Paiku Co. High inflow from monsoon precipitation and glacier melting and moderate lake evaporation, for instance, drove rapid lake-level increase during the monsoon season. In contrast, high lake evaporation and reduced inflow caused lake level to decrease significantly during the post-monsoon season. This study implies that lake evaporation may play an important role in the different amplitudes of seasonal lake-level variations on the TP.

Intra-Annual and Interannual Dynamics of Evaporation Over Western Lake Erie.

Evaporation (E) is a critical component of the water and energy budget in lake systems yet is challenging to quantify directly and continuously. We examined the magnitude and changes of E and its drivers over Lake Erie—the shallowest and most southern lake of the Laurentian Great Lakes. We deployed two eddy‐covariance tower sites in the western Lake Erie Basin—one located nearshore (CB) and one offshore (LI)—from September 2011 through May 2016. Monthly E varied from 5 to 120 mm, with maximum E occurring in August–October. The annual E was 635 ± 42 (±SD) mm at CB and 604 ± 32 mm at LI. Mean winter (October–March) E was 189 ± 61 mm at CB and 178 ± 25 mm at LI, accounting for 29.8% and 29.4% of annual E. Mean daily E was 1.8 mm during the coldest month (January) and 7.4 mm in the warmest month (July). Monthly E exhibited a strong positive linear relationship to the product of wind speed and vapor pressure deficit. Pronounced seasonal patterns in surface energy fluxes were observed with a 2‐month lag in E from R n, due to the lake's heat storage. This lag was shorter than reports regarding other Great Lakes. Difference in E between the offshore and nearshore sites reflected within‐lake spatial heterogeneity, likely attributable to climatic and bathymetric differences between them. These findings suggest that predictive models need to consider lake‐specific heat storage and spatial heterogeneity in order to accurately simulate lake E and its seasonal dynamics.

Estimating reservoir evaporation losses for the United States: Fusing remote sensing and modeling approaches

Evaporation from open surface water is a critical and continuous process in the water cycle. Globally, evaporation losses from reservoirs are estimated to be greater than the combined consumption from industrial and domestic water uses. However, this large volume of water loss is only coarsely considered in modern water resources management practices due to the complexities involved with quantifying these losses. By fusing remote sensing and modeling approaches, this study developed a novel method to accurately estimate the evaporation losses from 721 reservoirs in the contiguous United States (CONUS). Reservoir surface areas were extracted and enhanced from the Landsat based Global Surface Water Dataset (GSWD) from March 1984 to October 2015. The evaporation rate was modeled using the Penman Equation in which the lake heat storage term was considered. Validation results using in situ observations suggest that this approach can significantly improve the accuracy of the simulated monthly reservoir evaporation rate. The evaporation losses were subsequently estimated as the product of the surface area and evaporation rate. This paper presents a first of its kind, comprehensively validated, locally practical, and continentally consistent reservoir evaporation dataset. The results suggest that the long term averaged annual evaporation volume from these 721 reservoirs is 33.73 × 109 m3, which is equivalent to 93% of the annual public water supply of the United States (in 2010). An increasing trend of the evaporation rate (0.0076 mm/d/year) and a slightly decreasing trend of the total surface area (−0.011 × 109 m2/year) were both detected during the study period. As a result, the total evaporation shows an insignificant trend, yet with significant spatial heterogeneity. This new reservoir evaporation dataset can help facilitate more efficient water management practices.

Modelling Lake Titicaca's daily and monthly evaporation

Abstract. Lake Titicaca is a crucial water resource in the central part of the Andean mountain range, and it is one of the lakes most affected by climate warming. Since surface evaporation explains most of the lake's water losses, reliable estimates are paramount to the prediction of global warming impacts on Lake Titicaca and to the region's water resource planning and adaptation to climate change. Evaporation estimates were done in the past at monthly time steps and using the four methods as follows: water balance, heat balance, and the mass transfer and Penman's equations. The obtained annual evaporation values showed significant dispersion. This study used new, daily frequency hydro-meteorological measurements. Evaporation losses were calculated following the mentioned methods using both daily records and their monthly averages to assess the impact of higher temporal resolution data in the evaporation estimates. Changes in the lake heat storage needed for the heat balance method were estimated based on the morning water surface temperature, because convection during nights results in a well-mixed top layer every morning over a constant temperature depth. We found that the most reliable method for determining the annual lake evaporation was the heat balance approach, although the Penman equation allows for an easier implementation based on generally available meteorological parameters. The mean annual lake evaporation was found to be 1700 mm year−1. This value is considered an upper limit of the annual evaporation, since the main study period was abnormally warm. The obtained upper limit lowers by 200 mm year−1, the highest evaporation estimation obtained previously, thus reducing the uncertainty in the actual value. Regarding the evaporation estimates using daily and monthly averages, these resulted in minor differences for all methodologies.

Estimating daily lake evaporation from biweekly energy‐budget data

AbstractEstimates of daily lake evaporation based on energy‐budget data are poor because of large errors associated with quantifying change in lake heat storage over periods of less than about 10 days. Energy‐budget evaporation was determined during approximately biweekly periods at a northern Minnesota, USA, lake for 5 years. Various combinations of shortwave radiation, air temperature, wind speed, lake‐surface temperature, and vapour‐pressure difference were related to energy‐budget evaporation using linear‐regression models in an effort to determine daily evaporation without requiring the heat‐storage term. The model that combined the product of shortwave radiation and air temperature with the product of vapour‐pressure difference and wind speed provided the second best fit based on statistics but provided the best daily data based on comparisons with evaporation determined with the eddy‐covariance method. Best‐model daily values ranged from −0.6 to 7.1 mm/day over a 5‐year period. Daily averages of best‐model evaporation and eddy‐covariance evaporation were nearly identical for all 28 days of comparisons with a standard deviation of the differences between the two methods of 0.68 mm/day. Best‐model daily evaporation also was compared with two other evaporation models, Jensen–Haise and a mass‐transfer model. Best‐model daily values were substantially improved relative to Jensen–Haise and mass‐transfer values when daily values were summed over biweekly energy‐budget periods for comparison with energy‐budget results.

The interplay of local and regional factors in generating temporal changes in the ice phenology of Dickie Lake, south-central Ontario, Canada

Ice-on date occurred significantly later over 1975–2009 at Dickie Lake, Ontario, while ice-off date showed no significant trend, differing from many other records in North America. We examined the ice phenology using 3 modelling approaches: a lake-specific regression model to derive a suite of local predictors; a regionally derived regression model to test larger-scale predictors; and a physically based, one-dimensional thermodynamic model. All 3 models were also applied to generate future ice cover scenarios. The local regression revealed air temperature to be an important predictor of ice phenology in our area, as reported elsewhere; however, reductions in wind speed and increases in lake heat storage over the last 35 years also contributed significantly to a delayed ice-on date. Ice-off dates were strongly correlated with the effects of warmer air temperatures but also influenced by increased snowfall and reduced wind speed. Thus, although changes in ice phenology were related to continental-scale changes in air temperature, they were also influenced by more localized climatic variables, and a careful examination of local events was needed for a complete assessment of ice phenology. Predictabilities of the regional regression model, which primarily relied on air temperature to predict phenology, and the physically based model were lower than the lake-specific local regressions, reinforcing the need for inclusion of local variables when greater accuracy is important. Finally, the 3 methods generated similar estimates of reductions in ice cover over the next 90 years, predicting a 4050 day decrease in ice season length by 2100.

Shifting balance of thermokarst lake ice regimes across the Arctic Coastal Plain of northern Alaska

The balance of thermokarst lakes with bedfast‐ and floating‐ice regimes across Arctic lowlands regulates heat storage, permafrost thaw, winter‐water supply, and over‐wintering aquatic habitat. Using a time‐series of late‐winter synthetic aperture radar (SAR) imagery to distinguish lake ice regimes in two regions of the Arctic Coastal Plain of northern Alaska from 2003–2011, we found that 18% of the lakes had intermittent ice regimes, varying between bedfast‐ice and floating‐ice conditions. Comparing this dataset with a radar‐based lake classification from 1980 showed that 16% of the bedfast‐ice lakes had shifted to floating‐ice regimes. A simulated lake ice thinning trend of 1.5 cm/yr since 1978 is believed to be the primary factor driving this form of lake change. The most profound impacts of this regime shift in Arctic lakes may be an increase in the landscape‐scale thermal offset created by additional lake heat storage and its role in talik development in otherwise continuous permafrost as well as increases in over‐winter aquatic habitat and winter‐water supply.

Long-Term Study of Lake Evaporation and Evaluation of Seven Estimation Methods: Results from Dickie Lake, South-Central Ontario, Canada

Establishing satisfactory calculation methods of lake evaporation has been crucial for research and manage-ment of water resources and ecosystems. A 30 year dataset from Dickie Lake, south-central Ontario, Canada added to the limited long-term studies on lake evaporation. Evaporation during ice-free season was calcu-lated separately using seven evaporation methods, based on field meteorology, hydrology and lake water temperature data. Actual evaporation determined during a portion of a year was estimated using a lake en-ergy budget model, and the estimation was used as reference evaporation for evaluation of the seven methods. The deviation of method-induced evaporation from the reference evaporation was compared among the seven methods, and a performance rank was proposed based on the root mean squared deviation and coeffi-cient of efficiency. As for the whole ice-free season (roughly May to November), the water balance was the best method, followed by Makkink, DeBruin-Kejiman, Penman, Priestley-Taylor, Hamon, and Jensen-Haise methods. As for shorter duration (a week to a month), the DeBruin-Kejiman was the best method, followed by Penman, Priestley-Taylor, Makkink, Hamon, Jensen-Haise, and water balance method. Annual and sea-sonal changes of energy budget terms and the compensation function of lake heat storage in evaporation flux were also analyzed.

Surface energy balance calculations for small northern lakes

An energy balance model is used to determine diurnal surface energy balance components for three different sized high-latitude Canadian lakes in the Mackenzie River Basin (MRB) during the open water seasons of 2000, 2001, and 2002. Surface net radiation is derived from the component fluxes of the radiation balance. Turbulent heat fluxes are calculated using the aerodynamic method with input from local meteorological stations and experimentally derived drag coefficients. Lake heat storage, determined as a residual of the surface energy balance, is used together with measured water temperature profiles to calculate the daily mixing layer depth. The model uses readily available meteorological inputs for radiation calculations. Verification results for surface energy balance components show mean bias error (MBE) generally less than 5% of the mean measured daily fluxes and root mean square error (RMSE) less than 38%, which decreases to less than 16% for 10-day averaging periods. The model tends to overestimate net radiation by 7% and latent and sensible heat fluxes by about 4% and 1%, respectively, on average. Inferred slab layer depths indicate that the shallowest lake was isothermal while the deeper lakes showed temporal variations as expected. Copyright © 2006 Royal Meteorological Society.

PROBABILISTIC GREAT LAKES HYDROLOGY OUTLOOKS1

ABSTRACT: The Great Lakes Environmental Research Laboratory developed a semiautomatic software package for making hydrological outlooks for the Great Lakes. These include basin moisture storages, basin runoff, lake heat storage, lake evaporation, heat fluxes, and net lake supplies, one or more full months into the future. The package combines GLERL's rainfall‐runoff and lake evaporation models with near real‐time data reduction techniques to represent current system states. Users select historical meteorologic record segments as candidate future scenarios to generate deterministic near real‐time hydrological outlooks. GLERL has extended the package to make probabilistic outlooks for a decision‐maker who must estimate the risk associated with his decisions. GLERL matches National Weather Service meteorologic outlook probabilities by selecting groups of historical meteorologic sequences, and constructs embedded outlook intervals for each hydrologic variable of interest. Interval probabilities are assigned from comparisons over a recent evaluation period. This physically‐based approach for generating outlooks offers the ability, as compared to other statistically‐based approaches, to incorporate improvements in the understanding, of process dynamics as they occur in the future and to respond reasonably to conditions initial to a forecast (such as heat and moisture storages), not observed in the past.

Evaluation of the Energy Budget Method of determining evaporation at Williams Lake, Minnesota, using alternative instrumentation and study approaches

Best estimates of evaporation at Williams Lake, north central Minnesota, were determined by the energy budget method using optimum sensors and optimum placement of sensors. These best estimates are compared with estimates derived from using substitute data to determine the effect of using less accurate sensors, simpler methods, or remotely measured data. Calculations were made for approximately biweekly periods during five open water seasons. For most of the data substitutions that affected the Bowen ratio, new values of evaporation differed little from best estimates. The three data substitution methods that caused the largest deviations from the best evaporation estimates were (1) using changes in the daily average surface water temperature as an indicator of the lake heat storage term, (2) using shortwave radiation, air temperature, and atmospheric vapor pressure data from a site 110 km away, and (3) using an analog surface water temperature probe. Recalculations based on these data substitutions resulted in differences from the best estimates as much as 89%, 21%, and 10%, respectively. The data substitution method that provided evaporation values that most closely matched the best estimates was measurement of the lake heat storage term at one location in the lake, rather than at 16 locations. Evaporation values resulting from this substitution method usually were within 2% of the best estimates.

Testing lake energy budget models under varying atmospheric stability conditions

Several variations of a basic energy budget model were tested under varying atmospheric stability conditions using temperature data from Lake Mendota and meteorologic data from nearby Truax Airfield, Madison, Wisconsin. The flux enhancements predicted by Model 1 (Deardorff) for prevailing over-lake lapse conditions were inconsistent with measured changes in lake heat storage. When using the Budyko formulation for sky emissivity, ε, satisfactory energy residuals were obtained by eliminating the lapse enhancement while retaining the suppressive effects of over-lake inversions (Model 2 = modified Deardorff). Here, the best estimate of the 10 m Dalton coefficient was 1.45 × 10 −3 (cgs units; neutral profile). However, when the Koberg model for ε was adopted instead, satisfactory energy residuals were obtained only after eliminating all adjustments for non-neutral conditions, and increasing the 10 m Dalton coefficient to approximately 1.55 × 10 −3 (Model 3). Models 2 and 3 predicted annual evaporation from Lake Mendota of 71 and 86 cm during 1977 (including approximately 6 cm of sublimation during ice cover), bracketing earlier estimates for this locality (76 cm) based on U.S. Weather Bureau Class A pan data, and consistent with intensive studies of Pretty Lake in northern Indiana. My estimates of the 10 m Dalton coefficient (1.45 × 10 −3 to 1.55 × 10 −3) also narrowly bracket values for Lake Hefner and Lake Mead (1.49 × 10 −3), obtained in studies by the U.S. Geological Survey. Moreover, as in the case of the Will Rogers airport near Lake Hefner, meteorologic data collected at Truax Airfield, Wisconsin, proved adequate for estimating sensible and latent heat transfer over the adjacent lake.

Heat storage and advection in Lake Erie

Heat content and net advection based on long‐term monthly mean input data covering 17 yr (1952–1968) were derived for Lake Erie. The lake heat storage changes and net advection, with major components, are presented for the average monthly periods, indicating normal values for these parameters. Data limitations for the lake heat content precluded computation of monthly values by individual years. Derivation of the necessary input data (water temperature profiles, water supply and loss factors with appropriate temperatures, and ice conditions) is briefly described.