Energy Budget Method Research Articles

Instability of bubbly jets subjected to unrelaxed axial elastic tension

Injection of bubbly jets is a critical process in various fields, such as fuel atomization and petrochemicals. However, existing instability models for bubbly jets have predominantly focused on density variations due to bubble compressibility, largely neglecting the impact of bubbles on the macroscopic rheological properties of the mixture. In this study, we have integrated compressibility with non-Newtonian properties induced by bubbles to explore the evaluation of jet perturbations. Additionally, considering bubble pre-deformation before injection, we particularly examine the role of unrelaxed axial elastic tension in the bubbly jets. Both linear stability analysis and energy budget methods are used to illustrate the contributions of viscosity, elasticity, and compressibility. The results indicate that the viscoelastic effects induced by bubbles can significantly outweigh the effects of compressibility during the jet destabilization process. Notably, a slight unrelaxed tension can markedly increase both the perturbation growth rate and the cutoff wavenumber, potentially making it a more dominant driver of jet instability than the classical surface tension.

Estimating incident infrared radiation intensity on a horizontal surface

The study aims to characterize external IR heating sources, operating in free convection atmosphere, qualitatively and quantitatively for various applications. It employs non-invasive IR thermography to measure steady-state irradiations from a ceramic IR heater at variable voltages (60–150 V) using the surface energy budget (SEB) method which relies on only two measured parameters (surface and ambient temperature). The free convection heat transfer from the plate is demarcated between the thermal boundary layer (TBL) and buoyant plume-dominated region by temperature histogram tool. Nearly 78 ± 5 % of the plate area is occupied by the hot plume(s) in the studied voltage range. Estimated irradiation agrees fairly well with one another (within ± 10 %). Additionally, the time response of the plate was measured to be ∼ 120 s. This fast response can be made even faster, by reducing the thermal mass, eventually leading to low-cost IR sensors.

Artificial neural network and energy budget method to predict daily evaporation of Boudaroua reservoir (northern Morocco)

Evaporation is one of the main essential components of the hydrologic cycle. The study of this parameter has significant consequences for knowing reservoir level forecasts and water resource management. This study aimed to test the three artificial neural networks (feed-forward, Elman and nonlinear autoregressive network with exogenous inputs (NARX) models) and multiple linear regression to predict the rate of evaporation in the Boudaroua reservoir using the calculated values obtained from the energy budget method. The various combinations of meteorological data, including solar radiation, air temperature, relative humidity, and wind speed, are used for the training and testing of the model’s studies. The architecture that was finally chosen for three types of neural networks has the 4-10-1 structure, with contents of 4 neurons in the input layer, 10 neurons in the hidden layer and 1 neuron in the output layer. The calculated evaporation rate presents a typical annual cycle, with low values in winter and high values in summer. Moreover, air temperature and solar radiation were identified as meteorological variables that mostly influenced the rate of evaporation in this reservoir, with an annual average equal to 4.67 mm∙d –1. The performance evaluation criteria, including the coefficient of determination (R 2), root mean square error ( RMSE) and mean absolute error ( MAE) approved that all the networks studied were valid for the simulation of evaporation rate and gave better results than the multiple linear regression (MLR) models in the study area.

Analysis and Modelling of Temperature at the Water – Atmosphere Interface of a Lake by Energy Budget and ANNs Models

Different processes of lake surface water temperature (Tsw) are considered in this work. The Tsw estimation is based on the energy budget method and Artificial Neural Networks (ANNs models).These processes were applied to Vegoritis Lake in northern Greece. For the analysis, daily meteorological data, lake characteristics, as well as simulation results from an integrated heat transfer model were used for two complete years. The simulation results from the heat transfer model are considered as the reference and more accurate procedure to estimate Tsw. These results are used to compare the performance of the other processes. The examined processes include:(a) models of heat storage changes in relation to net radiation values Qt(Rn); (b) net radiation estimation using different approaches, such as the process of Slob’s equation with adjusted coefficients to lake data; and (c) ANN models with various architectures and input variables. The results show that the surface water energy budget model accurately describes the temperature (r2 = 0.916, RMSE = 2.422 °C). The ANN(5,6,1) model in which Tsw(i-1) is incorporated in the input variables was considered the best performing compared to all other ANN structures (r2 = 0.995, RMSE = 0.490 °C). Using different approaches for simulating net radiation (Rn) and Qt(Rn) in the equation of surface water temperature estimation provides results with lower accuracy.

Application of Arduino and CMOS temperature-humidity sensor to evapotranspiration calculation by Bowen ratio energy budget method

Application of Arduino and CMOS temperature-humidity sensor to evapotranspiration calculation by Bowen ratio energy budget method

Improving groundwater recharge estimates in alfalfa fields of New Mexico with actual evapotranspiration measurements

Quantifying groundwater recharge from irrigation practices of arid regions is necessary for efficient and sustainable groundwater resources management. Recharge is difficult to measure directly, many studies have quantified recharge from agricultural fields as a residual of the soil water balance method (WBM) or by other mathematical models estimating evapotranspiration (ET) and measuring soil moisture, rainfall, and irrigation. ET is often estimated using weather parameters from climate stations that are distant from crops. Flooding of fields is the most common form of irrigation used by farmers in the Mesilla Valley, New Mexico to grow alfalfa, one of the state’s major crops. The objectives of this study were to quantify recharge in flood irrigated alfalfa fields in the Mesilla Valley, New Mexico using the WBM and actual ET measurements during the 2017 growing season. The study fields were different sizes, crop ages, and soil textures. Actual ET of alfalfa was measured on the largest field using the eddy covariance − energy budget method and applied to the two other nearby fields as estimated ET. All other WBM parameters were measured at each study site (i.e. soil moisture, rainfall, and applied irrigation). Recharge using ET referenced to grass (ETsz) was then calculated using weather parameters and compared with measured ET. Recharge ranged from 618 to 716 mm with no significant statistical differences between the three alfalfa fields (f-ratio of 0.8876 and a p-value of 0.42 using ANOVA). Recharge to irrigation ratio ranged from 37% to 45%. On-farm irrigation efficiency ranged from 54.86% to 59.94%. When compared to measured ET, ETsz underestimated recharge of alfalfa by 11% in the WBM and overestimated recharge by 6% when a reduction in ETsz during harvest periods are considered. The results show that the measurement of actual ET improved recharge estimates in the alfalfa fields.

Pan coefficients for estimating open-water surface evaporation for a humid tropical monsoon climate region in India

Pan coefficients have been developed for the Sukhna lake region in Chandigarh, India that has a humid tropical monsoon climate, using the optimisation technique for annual, monthly and seasonal time scales. Evaporation estimated using the Bowen ratio energy budget method has been considered as actual evaporation. Results show that the pan coefficient for the study area varies significantly both by month and season. The month-wise variation is in the range of 0.72–1.40 and the seasonal variation is in the range of 0.81–1.16. Pan coefficients obtained using various existing models such as Cuenca, Snyder, Modified Snyder, Pereira, Orang, FAO-56 and Wahed–Snyder have also been compared with the developed coefficients. Comparative analysis indicates that the pan coefficients obtained using the Snyder model overestimate evaporation significantly, while the rest of the models significantly underestimate evaporation. The study concludes that the developed pan coefficients are observed to estimate the open-water surface evaporation with a fair degree of accuracy for the study area while the pan coefficient value of 0.7 being used by most field organisations in India give high errors. However, since pan coefficients vary spatially due to the variation in the relative significance of various meteorological parameters, the pan coefficients developed in the present study need to be further evaluated for their suitability to other similar climatic regions of India.

Evaluation of ten methods for estimating evaporation in a small high-elevation lake on the Tibetan Plateau

To quantify lake evaporation and its variations in time, ten methods for estimating evaporation at a temporal resolution of 10 days over a small high-elevation lake in the Nam Co lake basin of the Tibetan Plateau (TP) were evaluated by using eddy covariance (EC) observation-based reference datasets. After examination of the consistency of the parameters used in the different methods, the ranking of the methods under different conditions are shown to be inconsistent. The Bowen ratios derived from meteorological data and EC observations are consistent, and it supports a ranking of energy-budget-based methods (including the Bowen ratio energy budget, Penman, Priestley-Taylor, Brutsaert-Stricker and DeBruin-Keijman methods) as the best when heat storage in the water can be estimated accurately. The elevation-dependent psychometric constant can explain the differences between the Priestley-Taylor and DeBruin-Keijman methods. The Dalton-type methods (Dalton and Ryan-Harleman methods) and radiation-based method (Jensen-Haise) all improve significantly after parameter optimization, with better performance by the former than the latter. The deBruin method yields the largest error due to the poor relationship between evaporation and the drying power of the air. The good performance of the Makkink method, with no significant differences before and after optimization, indicates the importance of solar radiation and air temperature in estimation of lake evaporation. The Makkink method was used for long-term evaporation estimation due to lack of water temperature observations in lakes on the TP. Lastly, long-term evaporation during the open-water period (April 6 to November 15 from 1979 to 2015) were obtained; the mean bias was only 6%. A decreasing-increasing trend in lake evaporation with a turning point in 2004 was noted, and this trend corresponds to the published decreasing-increasing trend in reference evapotranspiration on the Tibetan Plateau and can be explained by variations in related meteorological variables.

Modeling the Distributions of Brightness Temperatures of a Cropland Study Area Using a Model that Combines Fast Radiosity and Energy Budget Methods

Land surface temperatures (LSTs) obtained from remote sensing data are crucial in monitoring the conditions of crops and urban heat islands. However, since retrieved LSTs represent only the average temperature states of pixels, the distributions of temperatures within individual pixels remain unknown. Such data cannot satisfy the requirements of applications such as precision agriculture. Therefore, in this paper, we propose a model that combines a fast radiosity model, the Radiosity Applicable to Porous IndiviDual Objects (RAPID) model, and energy budget methods to dynamically simulate brightness temperatures (BTs) over complex surfaces. This model represents a model-based tool that can be used to estimate temperature distributions using fine-scale visible as well as near-infrared (VNIR) data and temporal variations in meteorological conditions. The proposed model is tested over a study area in an artificial oasis in Northwestern China. The simulated BTs agree well with those measured with the Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER). The results reflect root mean squared errors (RMSEs) less than 1.6 °C and coefficients of determination (R2) greater than 0.7. In addition, compared to the leaf area index (LAI), this model displays high sensitivity to wind speed during validation. Although simplifications may be adopted for use in specific simulations, this proposed model can be used to support in situ measurements and to provide reference data over heterogeneous vegetation surfaces.

Evapotranspiration and water balance in a hot pepper (Capsicum frutescens L.) field during a dry season in the tropics

Evapotranspiration and water balance in a hot pepper (Capsicum frutescens L.) field during the 2nd dry season were analyzed in this study. Actual evapotranspiration (ET) was estimated by Bowen Ratio Energy Budget (BREB) method, potential evaporation (EP) was calculated by Penman method, and irrigation volume of water was measured manually. Meteorological instruments were installed in the experimental field during hot pepper cultivation. Leaf area index increased during the growing stages where the highest LAI of 1.65 in the generative stage. The daily average of ET was 1.94 and EP was 6.71 mm resulting in low Kc. The Kc values were significantly different between stage to stage under T-test analysis (α = 0.05). Moreover, Kc in every stage could be related to soil water content (SWC) in logarithmic function. Totally, ET during hot pepper cultivation was 179.19 mm, while rainfall was 180.0 mm and irrigation water was 27.42 mm. However, there was a water shortages during vegetative and generative stages. This study suggested that consumptive water of hot pepper was complimented by soil and groundwater under the condition of water shortages in the vegetative and generative stages during the 2nd dry season.

Dead Sea evaporation by eddy covariance measurements vs. aerodynamic, energy budget, Priestley–Taylor, and Penman estimates

Abstract. The Dead Sea is a terminal lake, located in an arid environment. Evaporation is the key component of the Dead Sea water budget and accounts for the main loss of water. So far, lake evaporation has been determined by indirect methods only and not measured directly. Consequently, the governing factors of evaporation are unknown. For the first time, long-term eddy covariance measurements were performed at the western Dead Sea shore for a period of 1 year by implementing a new concept for onshore lake evaporation measurements. To account for lake evaporation during offshore wind conditions, a robust and reliable multiple regression model was developed using the identified governing factors wind velocity and water vapour pressure deficit. An overall regression coefficient of 0.8 is achieved. The measurements show that the diurnal evaporation cycle is governed by three local wind systems: a lake breeze during daytime, strong downslope winds in the evening, and strong northerly along-valley flows during the night. After sunset, the strong winds cause half-hourly evaporation rates which are up to 100 % higher than during daytime. The median daily evaporation is 4.3 mm d−1 in July and 1.1 mm d−1 in December. The annual evaporation of the water surface at the measurement location was 994±88 mm a−1 from March 2014 until March 2015. Furthermore, the performance of indirect evaporation approaches was tested and compared to the measurements. The aerodynamic approach is applicable for sub-daily and multi-day calculations and attains correlation coefficients between 0.85 and 0.99. For the application of the Bowen ratio energy budget method and the Priestley–Taylor method, measurements of the heat storage term are inevitable on timescales up to 1 month. Otherwise strong seasonal biases occur. The Penman equation was adapted to calculate realistic evaporation, by using an empirically gained linear function for the heat storage term, achieving correlation coefficients between 0.92 and 0.97. In summary, this study introduces a new approach to measure lake evaporation with a station located at the shoreline, which is also transferable to other lakes. It provides the first directly measured Dead Sea evaporation rates as well as applicable methods for evaporation calculation. The first one enables us to further close the Dead Sea water budget, and the latter one enables us to facilitate water management in the region.

Modeling the Temporal Variability of Thermal Emissions From Row-Planted Scenes Using a Radiosity and Energy Budget Method

Land surface temperature (LST) is often needed for using remotely sensed data to study the surface energy budget and hydrological cycle. However, LST is challenging to measure and simulate because of its high sensitivity to atmospheric instability and solar angle, particularly over large-scale heterogeneous scenes. We propose a model that combines radiosity theory and an energy budget method for surface temperatures; we also explore the anisotropic behavior of row-planted crop emissions. The surface thermodynamic equilibrium state is fulfilled via the interaction between the 3-D radiative transfer calculations of the thermal-region radiosity-graphics combined model and the energy balance equation. Despite its shortcomings, such as the time-consuming calculations, the proposed model is feasible according to the results of an intercomparison and validation analysis. The intercomparison shows that the model exhibits similar performance, in terms of surface temperature calculations, to that of the soil-canopy observation, photochemistry and energy balance model (root-mean-square differences) of 0.59 °C and 1.77 °C for the leaf and soil components, respectively. Excellent agreement with the observed directional variation over summer maize canopies is also obtained, with $\text{R}^{2}$ values exceeding 0.6 and a mean RMSE of 0.32 °C. Thus, we recommend the new combined model as an option for explaining directional anisotropy due to its potential application to 3-D scenes.

Evaporation from a shallow, saline lake in the Nebraska Sandhills: Energy balance drivers of seasonal and interannual variability

Despite potential evaporation rates in excess of the local precipitation, dry climates often support saline lakes through groundwater inputs of water and associated solutes. These groundwater-fed lakes are important indicators of environmental change, in part because their shallow water levels and salinity are very sensitive to weather and climatic variability. Some of this sensitivity arises from high rates of open-water evaporation, which is a dominant but poorly quantified process for saline lakes. This study used the Bowen ratio energy budget method to calculate open-water evaporation rates for Alkali Lake, a saline lake in the Nebraska Sandhills region (central United States), where numerous groundwater-fed lakes occupy the landscape. Evaporation rates were measured during the warm season (May – October) over three consecutive years (2007–2009) to gain insights into the climatic and limnological factors driving evaporation, as well as the partitioning of energy balance components at seasonal and interannual time scales. Results show a seasonal peak in evaporation rate in late June of 7.0mmday−1 (on average), with a maximum daily rate of 10.5mmday−1 and a 3-year mean July-September (JAS) rate of 5.1mmday−1, which greatly exceeds the long-term JAS precipitation rate of 1.3mmday−1. Seasonal variability in lake evaporation closely follows that of net radiation and lake surface temperature, with sensible heat flux and heat storage variations being relatively small, except in response to short-term, synoptic events. Interannual changes in the surface energy balance were weak, by comparison, although a 6-fold increase in mean lake level over the three years (0.05–0.30m) led to greater heat storage within the lake, an enhanced JAS lake-air temperature gradient, and greater sensible heat loss. These large variations in water level were also associated with large changes in absolute salinity (from 28 to 118gkg−1), with periods of high salinity characterized by reductions in mass transfer estimates of evaporation rate by up to 20%, depending on atmospheric conditions and absolute salinity. Energy balance estimates of evaporation, on the other hand, were found to be less sensitive to variations in salinity. These results provide regional insights for lakes in the Nebraska Sandhills region and implications for estimation of the energy and water balance of saline lakes in similar arid and semi-arid landscapes.

Theoretical analysis of reservoir-based floating photovoltaic plant for 15-khordad dam in Delijan

The current study presents the design features and photovoltaic requirements of a floating photovoltaic plant (FPVP) whose purpose is to reduce the evaporation from the surface of a water reservoir while generating electricity. A summary of the energy budget method is also introduced to calculate the rate of evaporation from the water reservoir behind 15-Khordad dam. The top of the reservoir has a surface area about 1.59 km2 but only 2% of it has been covered with the proposed FPVP with a stated capacity of 1.45 MWdc. The study proves that covering even a small percentage of the reservoir’s surface has a significant effect on the amount of water saved annually. Finally, the average water saved monthly due to FPVP, the electricity generated by the system in the first year, and the CO2 balance of the facility are calculated based on meteorological data of Delijan.

Artificial neural networks and empirical equations to estimate daily evaporation: application to Lake Vegoritis, Greece

ABSTRACTEvaporation is one of the most important components in the energy and water budgets of lakes and is a primary process of water loss from their surfaces. An artificial neural network (ANN) technique is used in this study to estimate daily evaporation from Lake Vegoritis in northern Greece and is compared with the classical empirical methods of Penman, Priestley-Taylor and the mass transfer method. Estimation of the evaporation over the lake is based on the energy budget method in combination with a mathematical model of water temperature distribution in the lake. Daily datasets of air temperature, relative humidity, wind velocity, sunshine hours and evaporation are used for training and testing of ANN models. Several input combinations and different ANN architectures are tested to detect the most suitable model for predicting lake evaporation. The best structure obtained for the ANN evaporation model is 4-4-1, with root mean square error (RMSE) from 0.69 to 1.35 mm d−1 and correlation coefficient from 0.79 to 0.92.EDITOR M.C. AcremanASSOCIATE EDITOR not assigned

Entrainment and mixing in unsteady gravity currents

ABSTRACTEntrainment and mixing in lock-exchange gravity currents are investigated by large eddy simulations. Nine cases are analysed, varying the initial excess density driving the motion and the aspect ratio r of the initial water depth to the lock length. Laboratory experiments are also performed and a fair agreement between numerical simulations and measurements is found. Mixing between the gravity current and the ambient fluid, in both the slumping and self-similar phases, is studied for a range of entrainment parameters, gravity current fractional area and using an energy budget method. The entrainment is found to increase as r decreases. The occurrence of irreversible mixing is detected during the entire development of the flow, i.e. both in the slumping and self-similar phases. A higher amount of mixing is observed as r decreases and the initial excess density increases.

Mixing in lock-release gravity currents propagating up a slope

Lock-exchange gravity currents propagating up a slope are investigated by large eddy simulations, focusing on the entrainment and mixing processes occurring between the dense current and the ambient fluid. Relevant parameters, such as the aspect ratio of the initial volume of dense fluid in the lock R, the angle between the bottom boundary and the horizontal direction θ and the depth aspect ratio ϕ, are varied. The numerical results are compared with laboratory experiments and a good agreement is found. Entrainment and mixing in a lock-release gravity current are studied using different entrainment parameters and an energy budget method. The entrainment is found to depend on both Froude, Fr, and Reynolds, Re, numbers. In addition, the dependence of both entrainment and mixing on the parameters varied is discussed. The entrainment decreases with increasing steepness of the bottom and R. Irreversible mixing is not affected by the varied parameters during the slumping phase, while during the successive phases of motion, it is found to decrease with the increase of θ and R. Low entrainment and mixing occur for ϕ < 1.

Evaporation Rate of a White Class A Evaporation Pan

AbstractThis study experimentally investigates the influence of color on the evaporation rate of a Class A evaporation pan. Two Class A evaporation pans, one in the original galvanized metal color and the other painted white, are placed in the same meteorological station for 18 months. Since the wind speed, air temperature, and vapor pressure deficit are the same for both pans, the color and the resulting net radiation are the only causes for differences in the evaporation rate. The results reveal that the average net radiation of the white pan is about 90% that of the metal-colored pan. This leads to the annual evaporation rate of the white pan (1,041 mm year−1) being only 75% of the evaporation rate (1,392 mm year−1) of the metal-colored pan. In addition, the prediction error of the daily evaporation rates by the energy budget method is lower than that of the Penman-Monteith type models. The differences between the measured evaporation rates of the two pans are analyzed to examine the role of irradian...

Numerical analysis of the combined rainfall-runoff process and snowmelt for the Alun River Basin, Heilongjiang, China

An accurate assessment of surface water resources would assist land and resource managers in any region. The objectives of this study were to develop a distributed hydrological numerical model for the calculation of rainfall-runoff when combined with snowmelt and to provide a practical method for estimating surface water resources in the semiarid area of western Heilongjiang Province, China. The Alun River Basin, with typical meteorological and hydrological characteristics of a semiarid area of western Heilongjiang Province, was chosen as the study area. Modeling of the vertical soil profile was conducted based on the investigation of physical properties of the underlying topography. A digital elevation model (DEM) and a map of the river channel network of the study area were generated by ArcMap in ArcGIS. Rainfall-runoff and snowmelt modules were developed using kinematic wave equations and the energy budget method, respectively. A distributed hydrological model for combining the snowmelt and the rainfall-runoff modules was developed using Fortran software. Numerical simulation of the observed river channel flow allowed model validation. Both annual and monthly runoff, runoff coefficient, and snowmelt runoff amounts were estimated through analyzing runoff calculation results from 2012 and 2013. The results indicated that the calculation accuracy of the model was within the allowable range of the error criterion (<0.03), the model exhibited relatively high efficiency, and the Nash–Sutcliffe efficiency (NSE) was more than 0.94; the annual runoff coefficients for 2012 and 2013 were 0.35 and 0.43, respectively; the runoff of the main snowmelt period (Mar 1 to Apr 15) accounted for 0.87 and 1.46 % of total annual runoff in 2012 and 2013, respectively. The results should provide a method that can be used for the accurate assessment of surface water resources and may provide the basis for the development of a numerical platform for estimating hydrological processes in the semiarid area of western Heilongjiang Province.

Evaporation in a Mediterranean environment by energy budget and Penman methods, Lake Baratz, Sardinia, Italy

Abstract. In Mediterranean environments, evaporation is a key component of lake water budgets. This applies to Lake Baratz in Sardinia, Italy, a closed lake that almost dried up in 2008 after a succession of years with low seasonal rainfall. We used the energy budget method and Penman's equation to estimate evaporation over Lake Baratz. We measured, using a raft station, water temperature at the surface, at 1, 2, 4, 6 m depth and at the bottom of the lake, as well as air temperature, relative humidity, wind speed, and net radiation over a period of 3 years. We also compared Penman's equation and the energy budget method in two other climatic zones using published data. Our results indicate that mean yearly evaporation over Lake Baratz was 950 mm. On an annual scale, evaporation estimated by Penman's method omitting heat storage as is usually done was 18% higher than by the energy budget method that included heat storage, with monthly differences ranging between −38 and +60%. Including the heat storage term in Penman's equation changed the monthly values but did not change the yearly value significantly. Solar radiation and heat storage were found to be the most important energy fluxes to and from the lake and had the greatest effect on evaporation rates for the energy budget method. The bias between the two methods has a seasonal cycle due to the storage and release of energy from the lake. Energy advected to and from the lake by precipitation, surface water and ground water had minor effect on evaporation rates. Lake Baratz, like other lakes in a Mediterranean environment, is particularly sensitive to the summer hot and dry climate. In contrast, we found that rates of evaporation estimated from Penman and the energy budget methods over tropical African lakes were nearly constant over the entire year and the difference between the two methods smaller. Difference between the two methods for North American lakes is also smaller probably owing to the ice-cover season and to lower radiation and lower temperatures during summer.