Energy Budget Method Research Articles

Regional Surface Fluxes From Remotely Sensed Skin Temperature and Lower Boundary Layer Measurements

During First International Satellite Land Surface Climatology Project Field Experiment in north‐eastern Kansas, surface temperature was measured by infrared radiation thermometers at some 12 stations spread over the 15 × 15 km experimental area. These data, together with wind and temperature profiles in the unstable atmospheric boundary layer measured by means of radiosondes, were analyzed within the framework of Monin‐Obukhov similarity. The radiometric scalar roughness corresponding to the radiometric surface temperature was found to increase as the season progressed; for the spring campaign the mean value was zoh,r = 4.56 × 10−7 m and for the fall zoh, r = 1.01 × 10 −2 m. The radiometric scalar roughness could also be expressed as a function of solar elevation and to a lesser extent, of canopy height or leaf area index. For an elevation range 10° ≤ α ≤ 75° the regression equation is zoh,r = exp [−0.735 ‐ 3.61 tan (α)]. With this function good agreement (r = 0.87) was obtained between the profile‐derived regional surface flux of sensible heat and the mean flux measured independently at ground‐based stations under unstable conditions. Similarly, regional values of evaporation, obtained by means of the energy budget method from these sensible heat flux estimates, were in good agreement (r = 0.96).

Estimation of transpiration by single trees: comparison of a ventilated chamber, leaf energy budgets and a combination equation

Ventilated chambers have been used to measure transpiration rates of various Eucalyptus species. However the microclimate within a chamber differs from natural conditions, leading to possible bias in the measurements. The validity of transpiration rates measured by ventilated chambers was assessed using two techniques which could be applied both with and without the chamber in place. The Penman-Monteith equation, applied to single leaves, provided one set of transpiration estimates for both chamber positions. A second set was obtained using a leaf energy budget method which utilized paired leaves, one of which was prevented from transpiring, while the other behaved normally. Temperature differences between the two leaves and boundary layer conductances measured in situ were used to estimate transpiration rates for normal leaves through solution of leaf energy budget equations. Transpiration rates within the ventilated chamber were reduced by up to 30% around midday relative to undisturbed conditions, according to estimates using the Penman-Monteith equation. Enhanced transpiration during late afternoon was also predicted. Diminished transpiration rates within the ventilated chamber were caused by a marked reduction in available energy when the chamber walls were raised. Recommendations are presented for techniques to measure net radiation absorbed by leaves within a tree canopy. Leaf energy budget measurements on 9–12 paired leaves did not confirm predictions from the Penman-Monteith equation that transpiration rates within the ventilated chamber were lower than under natural conditions. Midday transpiration measurements from leaf energy budgets were ∼ 25% higher than Penman-Monteith predictions when the ventilated chamber was in position and ∼ 25% lower when it was down, thus suggesting little change in transpiration rates with chamber position. Small differences in transpiration rates between trees cannot readily be resolved by any of the estimation techniques used in this study because of inherent experimental uncertainties in each method.

Harbeck research files donated

The collected papers and research files of G. Earl Harbeck (deceased), noted U.S. Geological Survey (USGS) research hydraulic engineer, have recently been donated by the USGS Gulf Coast Hydroscience Center to the Department of Civil Engineering at the University of Mississippi (University, Miss.). Harbeck performed important research in evaporation and evapotranspiration phenomena during the 1950s and 1960s that led to modern water and energy budget methods for lakes, streams, and reservoirs that are widely used today. Many of the papers in his files are unique; others have importance in the historical progression of evaporation research in lakes. Researchers or students interested in gaining access to the files may contact Robert M. Hackett, Chairman, Department of Civil Engineering, University of Mississippi, University, MS 38677, for details.

Developments in geothermal energy in Mexico—part ten: solar evaporation applied to chemical recovery from cerro prieto I brines

The waste brine from the Cerro Prieto geothermal field contains about 26,000 mg kg −1 of dissolved salts, mainly NaCl, KCl, CaCl 2 and LiCl. Since 1968, theoretical and experimental studies have been carried out, in order to find a process to recover some of these chemical products; in all the studies, concentrations of brine in solar ponds has been considered as the only economical way to crystallize NaCl and KCl. Results of these studies are described in this paper. Salt concentration curves against specific gravity in brine are reported. An evaporation ratio was calculated with evaporation rate measurements in water and brines at three specific gravities. From meteorological data, the evaporation rate for the Cerro Prieto area was calculated by the energy budget method and compared against measured values. A diffusional factor as a function of wind velocity, was obtained to calculate evaporation rates by the mass balance method.

An introduction to the European Hydrological System — Systeme Hydrologique Europeen, “SHE”, 2: Structure of a physically-based, distributed modelling system

The paper forms the second part of an introduction to the SHE, a physically-based, distributed catchment modelling system produced jointly by the Danish Hydraulic Institute, the British Institute of Hydrology and SOGREAH (France) with the financial support of the Commission of the European Communities. The SHE is physically-based in the sense that the hydrological processes of water movement are modelled either by finite difference representations of the partial differential equations of mass, momentum and energy conservation, or by empirical equations derived from independent experimental research. Spatial distribution of catchment parameters, rainfall input and hydrological response is achieved in the horizontal by an orthogonal grid network and in the vertical by a column of horizontal layers at each grid square. Each of the primary processes of the land phase of the hydrological cycle is modelled in a separate component as follows: interception, by the Rutter accounting procedure; evapotranspiration, by the Penman-Monteith equation; overland and channel flow, by simplifications of the St. Venant equations; unsaturated zone flow, by the one-dimensional Richards equation; saturated zone flow, by the two-dimensional Boussinesq equation; snowmelt, by an energy budget method. Overall control of the parallel running of the components and the information exchanges between them is managed by a FRAME component. Careful attention has been devoted to a modular construction so that improvements or additional components (e.g. water quality and sediment yield) can be added in the future. Considerable operating flexibility is provided through the ability to vary the level of sophistication of the calculation mode to match the availability or quality of the data.

Use of the chloride ion in determining hydrologic-basin water budgets — A 3-year case study in the San Juan Mountains, Colorado, U.S.A.

Measurement of chloride concentration and water equivalent in precipitation and recharge at a site can be extrapolated to determine available moisture in a nearby basin. This method also may be extrapolated to a basin with similar climatic characteristics if precipitation, vegetation, and topographic data are available. The average accuracy of the total of evaporation, recharge, and runoff (assuming no storage) was about 10% of total precipitation. Soil-moisture measurements indicate the entire 10% error in moisture balance can be attributed to annual changes in storage. Data requirements for the method are considerably less than data requirements for energy-budget methods to determine available moisture. Potential applications of the method to hydrologic problem-solving are: 1. (1) Estimating total available moisture from chloride concentrations in groundwater or surface water or both. 2. (2) Modeling paleoclimate scenarios and evaluating their correctness by comparison with paleo-groundwater chloride concentrations. 3. (3) Providing an independent comparison for water budgets obtained by energy-budget methods. Obviously the method cannot be applied readily to systems with a lithologic source of chloride. Most systems primarily consisting of tuff, intrusive volcanic rock, nonmarine sediments, quartzite, and other metamorphic rocks will be suitable for application of the model.

The water and energy balances of Perch Lake (1969–1980)

Abstract Since 1969, meteorological and limnological measurements required for evaporation estimates by the energy budget method have been made almost continuously during the open water season at Perch Lake, a small (0.45 km2), shallow (mean depth 2 m) lake on the Canadian Shield. Hydrological measurements required for water budget calculations have been made continuously since 1970. Since ground water input to the lake has been found to be significant, energy budget estimates of evaporation are used in the water budget equation to estimate ground water inflow. Results are summarized as the long‐term averages along with the ranges of variation of the budget components observed during the eleven‐year period.

Comparison of hydrologically simulated and remotely sensed actual evapotranspiration from some Mediterranean vegetation formations

Abstract Actual evapotranspiration (AET) estimates representing four Mediterranean vegetation formations (from shrubland to dense woodland) have been obtained using a physically-based hydrological model and a simplified residual energy budget method applied to HCMM satellite sensor data. A good agreement between simulated and remotely sensed AET values has been obtained. Results are discussed with reference to roughness scaling lengths for momentum and heat.

A new method for the estimation of diffusive resistance of leaves

The measurement of diffusive resistance in leaves is a difficult task, and is frequently accomplished with diffusion porometers. A new energy budget method is shown, where the internal diffusive resistance, the aerodynamic resistance, and the absorbed radiation may be estimated using the temperature of three leaves, the air temperature, and the relative humidity or vapor pressure deficit. Of the three leaves, one is coated with a substance impervious to water, one with water, and one is left uncoated. Absorbed solar irradiances in the 400 to 1100 nm wavelength region for coated leaves were within 2% and 6% of uncoated leaves for adaxial and abaxial surfaces, respectively. The methodology was tested on soybean plants with diffusion porometry used as a reference. The results showed a good correspondence between the two methods, with only as much scatter as reported in inter-porometer comparisons. The method presented here may be developed for automatic unattended operation.

Predicting Soil Temperature and Soil Heat Flux under Different Tillage‐Surface Residue Conditions

AbstractModel descriptions for soil temperature utilizing readily available information are needed to project management effects of tillage. In many cases these model descriptions must cover periods of a month or more during the growing season. A procedure was developed to utilize daily maximum and minimum air temperature along with normalized root zone temperatures. Root zone temperatures were much more sensitive to the surface residue than the surface roughness (or other tilled layer property) characteristic of tillage‐residue cover combinations. However, root zone temperatures normalized with respect to daily maximum and minimum temperatures were of a similar shape for all tillage‐residue cover combinations. These normalized soil temperatures also afforded easy comparison among treatments and locations. A Fourier series analysis of daily normalized soil temperatures averaged over part of a growing season showed that the average value around which average normalized soil‐temperature curves (diurnal wave) oscillate varies with depth and season. Amplitudes and phase angles of the first two harmonics of the Fourier series were approximately the same for all treatments over four seasons.A model was developed to estimate soil temperatures for various tillage‐residue cover treatments with and without a crop cover for the northern Corn Belt states. The model utilizes the first two harmonics of the Fourier series and the relationships between the daily maximum and minimum soil surface temperatures vs. maximum and minimum air temperatures. Input needed for the model are: daily maximum and minimum air temperatures, thermal diffusivity of soil, and coefficients of the Fourier series fitted to average normalized soil temperatures. At one location in southern Minnesota the model predicted soil temperatures at 0.05 and 0.10‐m depths over 45 d during the spring of 1980 within an average difference of 2.0°C and a deviation of no more than 3.8°C 67% of the time.A procedure to estimate hourly soil surface heat flux under different tillage and residue conditions is also presented. The procedure is based on the Fourier series soil temperature model. Inputs needed for the model are: (i) daily maximum and minimum air temperatures, (ii) thermal diffusivity, and (iii) volumetric heat capacity. Soil surface heat flux is often needed in the calculation of evaporation from the energy budget methods.

The measurement of evaporation by meteorological methods

Three methods based on energy budget and turbulent transfer formulations may be recommended for the determination of evaporation E from catchment areas. They all involve measurement of available energy R-G, R being net radiative flux and G the heat flux into the surface. When estimates from forests on an hourly to daily basis are made, the contribution from canopy heat storage should be included in G. The energy budget/Bowen ratio method requires no detailed specification of surface properties but involves relatively complex instrumentation to measure vertical differences of temperature and humidity in the air. With the exclusion of eddy covariance, it is potentially the most accurate method and should be applicable for crops and forests, over a wide range of evaporation conditions. The residual energy budget method requires accurate estimates of atmospheric resistance and measurement of surface temperature. Where the latter is available (by airborne radiometer) the method is most reliable for surfaces of low roughness or in conditions of high evaporation. The combination method incorporates both energy budget and bulk relationships to eliminate surface temperature. It introduces surface resistance, which must be parameterized in terms of soil, plant species and atmospheric quantities, with allowance made for sub-canopy fluxes and evporation of intercepted rainfall. The method is suitable for estimating daily or monthly evaporation using standard atmospheric observations. The eddy covariance method is not yet sufficiently developed to measure E reliably at the operational level over long periods of time and over less-than uniform terrain but, of all the methods to be described, it has the greatest potential to do so. Methods based on eddy covariance, wind and other profiles are more appropriate to research investigations and, with the above, are described in the text.

The Priestley-Taylor Evaporation Model Applied to a Large, Shallow Lake in the Netherlands

The applicability of the model of Priestley and Taylor (1972) for evaporation of saturated surfaces is examined for the former Lake Flevo (The Netherlands). This lake had an area of about 460 km2 and an average depth of 3 m. Daily values of evaporation in the period July–September 1967, determined with the energy-budget method, are compared with the corresponding estimated values obtained by the Priestley-Taylor model. The agreement appears to be satisfactory. The diurnal variation of the parameter α of the Priestley-Taylor model is found to be pronounced. From standard meteorological observations at Oostvaardersdiep, a station at the perimeter of the lake, and an energy-budget model of Keijman (1974) an indirect extension of the available time series is obtained. In this way energy-budget data for the period April–October 1967 became available. Analysis of this data set leads to the preliminary conclusion that α has a seasonal variation. This is due to the fact that there is a linear relation between the daily latent heat flux LE and the equilibrium latent heat flux LEEQ with a nonzero intercept.

An advection‐aridity approach to estimate actual regional evapotranspiration

Actual regional evapotranspiration is calculated by means of a procedure requiring only meteorological data, which are those commonly used in the various versions of the combination approach for potential evaporation. The approach is based on a conceptual model involving, first, the effect of regional advection on potential evaporation, and second, an assumed symmetry between potential and actual evaporation with respect to the evaporative power of the air in the absence of advection. Thus the degree of nonavailability of water for evapotranspiration, that is the aridity of the region, is deduced from the regional advection of drying power of the air, as implied by the atmospheric conditions. The approach was found to give good agreement with daily data of evapotranspiration obtained by means of an energy budget method for a period of severe drought in a rural watershed in a sandy region. One of the advantages is that no soil moisture data, no stomatal resistance properties of the vegetation, nor any other additional aridity parameters are required to determine actual evapotranspiration.

Multiple Estimates of Lake Erie Evaporation

Evaporation from large lakes cannot be measured directly, but several methods have been developed to compute lake evaporation. Because of the Great Lakes data limitations, evaporation determined by a single method is’ not sufficiently reliable and requires verification of accuracy by different methods. Monthly evaporation from Lake Erie was derived by the water budget, selected mass transfer, and the energy budget approaches. The period of record varies with the availability of data, 1937-68 for the water budget and mass transfer methods, and 1952-1968 for the energy budget method. Evaporation determined by the water budget method was used to provide control for the other methods. The evaporation rates varied from -9 to 25 cm/month with periods of low, median, and high annual evaporation averaging approximately 80, 90 and 100 cm. The analysis of results indicates that reasonably accurate evaporation estimates during the year can be obtained by the water budget and the modified Lake Hefner mass-transfer equations.

Estimating energy budget components to determine Lake Huron evaporation

Evaporation is estimated for Lake Huron by the energy budget method and compared to available mass transfer estimates. Data were from representative shoreline station measurements and vessel cruise measurements. Agreement between evaporation by the energy budget and by mass transfer was reasonable from February through July with the exception of May when measurement of the heat content was a problem. For the remainder of the year the disparity is marked. The principal difficulty encountered was the lack of meteorological measurements on the lake or adequate techniques to extrapolate the quantities from shoreline data. Quantitative monthly values for each component in the budget equation are the first published for Lake Huron and one of the few sets available for the Great Lakes.

Network density of temperature profile stations and its influence on the accuracy of lake evaporation calculations

The accuracy of lake evaporation determined by the energy budget method depends on the precision of measurement of the total thermal energy content of the lake, which in turn is related to the number and distribution of the temperature‐measuring points. The number of sampling points to be used should be such that the error in the stored thermal energy is of the same magnitude as the error in the other terms in the energy budget. This problem was studied at Lake Hefner, a 2600‐acre off‐stream reservoir at Oklahoma City, Oklahoma. Ten evaporation periods of 1‐week duration each were included. Stored thermal energy was calculated on the basis of temperature profiles taken at 5‐foot depth increments at 19 locations uniformly spaced over the lake. Evaporation was determined by the energy budget method using stored thermal energy calculated on the basis of 1, 5, 11, or 19 temperature profile stations. Analysis showed the optimum number of stations to be 5, or one station per 520 acres. Using only one station resulted in an evaporation error of 8.2% at the deepest point of the lake. Increasing the number of stations from 5 to 19 resulted in an increase of accuracy of evaporation measurement of only 1%.

Micrometeorological energy budget methods and apparent diffusivity for Boreal forest and grass sites at Pinawa, Manitoba, Canada

A modified energy balance method which gives good engineering estimates of total daily and monthly latent and sensible heat flux for a forest canopy is described. On-line computer calculation of evapotranspiration is practicable. Monthly potential evapotranspiration was found by the Thornthwaite and Penman methods for a nearby grass site for comparison. A crude water budget for the year was also obtained.Regression lines of mean diffusivity on potential temperature gradient, wind and net radiation suggest that all three are equally good predictors of diffusivity. For inversion conditions diffusivity is not related to Richardson's number but is well correlated with potential temperature gradient (r = −0.5 to −0.7).This is part of a comprehensive study of gamma irradiation effects on Boreal forest plants at the Whiteshell Nuclear Research Establishment, Pinawa, Manitoba, Canada.

Evapotranspiration and Energy Balances of Forest and Field

The energy and water balance components of a 70‐year‐old Norway spruce forest, a 2‐year‐old alfalfa field, and a potato field near Munich, Germany, were computed for the period May–October 1965 by using hourly averages of metorologic parameters. Turbulent diffusion and energy budget methods were used to determine evapotranspiration and convective exchange. The two methods yielded satisfactory, agreement for the low crops but not for the forest. The mean seasonal albedo values for the potatoes and the alfalfa were 0.18 and 022, respectively. The albedo of the forest was obtained for 1 day and averaged 0.05. The shortwave incoming radiation over the forest was 12% less than that over the fields. The net shortwave radiation over the forest was 2 and 7% greater than that over the potatoes and the alfalfa, respectively, whereas the long wave emission from the forest was 22 and 15% less than that from the potatoes and the alfalfa, respectively. The total net radiation over the forest was 20% greater than that over the alfalfa and 16% greater than that over the potatoes. Sensible heat flux from the forest was 2.6 and 1.6 times greater than that from the alfalfa and the potatoes, respectively. Evapotranspiration from the forest was 4% less than that from the alfalfa but 14% greater than that from the potatoes. The roughness lengths of the forest and the fields were about 0.1 of their heights. The zero plane displacements were 0.71 and 0.5–0.6 of the heights of the forest and the crops, respectively. The exchange coefficient at the top of the trees was about 100 times as large as that at the tap of the crops. The water supply in the soil was not limiting on any of the three experimental sites during the vegetation period.

Present Day Evaporation Measurement Techniques

The energy-budget and mass-transfer methods are currently being used by the United States Geological Survey to measure evaporation from lakes and reservoirs. Because the field equipment is expensive and data processing and analysis are time consuming, the use of the energy-budget method is limited to those reservoirs where the need for detailed information warrants the expense. Ordinarily the mass-transfer coefficient for a selected reservoir is determined using the energy-budget method over a period of 15 months or longer. After this, the energy-budget equipment can be removed, and the mass-transfer method, which requires a minimum of equipment and office work, can be used to compute evaporation on a continuing basis. During 1965-67 a cooperative study by the International Boundary and Water Commission and the Geological Survey showed that evaporation from Falcon Reservoir on the Rio Grande was 189 cm and 167 cm for two successive years.

Transpiration Resistance of Plants

An energy budget method is described for using potom- eters to measure the minimum diffusion resistance to transpiration of excised leaves. The method is used to infer the transpiration rate of intact leaves in situ. Values of minimum resistance are given for several coniferous and deciduous trees and shrubs from wet to dry habitats. energy between the leaf and the environment by radiation, convection, and transpiration. The loss of water vapor by a leaf cools a leaf and often keeps the temperature from rising too high for plant proteins when the incident energy is large. During transpiration, water vapor diffuses from the mesophyll cell walls lining the substomatal cavity, through the stomatal channel, to the free air beyond the leaf. In still air there is a boundary layer of moist air adjacent to the leaf surface. The transpiration rate is proportional to the vapor pressure gradient between the mesophyll cell walls and the free air beyond the leaf, and is inversely proportional to the resistance to flow offered by the stomatal channel and boundary layer. It is the purpose of this paper to describe a method of measurement of the diffusion resistance of intact leaves or branches of plants. During the daytime, plants receive direct solar radiation and in- direct solar radiation scattered by the sky and clouds and reflected from the ground and nearby objects. They also receive thermal radia- tion emitted by the atmosphere, the ground and nearby objects. A certain fraction of the incident radiation is absorbed. Leaf tempera- ture adjusts to the energy exchange until the absorbed radiation absR, is balanced by the loss by reradiation, R, the loss or gain by convec- tion, C, and the loss by transpiration, E. The energy budget of a plant is discussed in detail by Gates (1962) and is written as follows: