Surface Energy Balance Equation Research Articles

The May?October energy budget of a Scots pine plantation at Hartheim, Germany

This paper describes measurements of the Hartheim forest energy budget for the 157-day period of May 11 – Oct. 14, 1992. Data were collected as 30-min means. Energy available to the forest was measured with net radiometers and soil heat flux discs; sensible heat exchange between the canopy and atmosphere was measured with two “One-Propeller Eddy Correlation” (OPEC) systems, and latent energy (evapotranspiration orET) was determined as a residual in the surface energy balance equation. Net rediation, change in thermal storage, and sensible heat flux were verified by independent measurements during the Hartheim Experiment (HartX, May 11–12), and again during the “HartX2” experiment over 20 days late in the summer (Sep. 10–29). Specifically, sensible heat estimates from the two adjacent OPEC sensor sets were in close agreement throughout the summer, and in excellent agreement with measurements of sonic eddy correlation systems in May and September. The eddy correlation/energy balance technique was observed to overestimate occurrence of dew, leading to an underestimate of dailyET of about 5%. After taking dew into account, estimates of OPECET totaled 358 mm over the 5.1-month period, which is in quite good agreement with an ET estimate of 328 mm from a hydrologic water balance. An observed decrease in forestET in July and August was clearly associated with low rainfall and increased soil water deficit. The OPEC system required only modest technical supervision, and generated a data yield of 99.5% over the period DOY 144–288. The documented verification and precision of this energy budget appears to be unmatched by any other long-term forest study reported to date.

Estimation of land surface parameters using satellite data

AbstractSurface observations and NOAA advanced very high resolution radiometer (AVHRR) satellite data are combined to provide area‐averaged values of albedo, canopy resistance, leaf area index and fractional vegetation cover. Albedo, fractional vegetation cover and leaf area index are derived from the reflectance of the visible and infra‐red NOAA AVHRR channels. Canopy resistance is estimated by closing the surface energy balance equation using the surface infra‐red temperature and the normalized difference vegetation index. These land surface parameters are evaluated against independent measurements and used as input into a numerical model to simulate the energy exchange between the surface and the overlying atmosphere. Simulation results are validated against detailed aircraft observations undertaken in south‐western Australia over both natural and agricultural vegetation.

Surface energy balance estimates at local and regional scales using optical remote sensing from an aircraft platform and atmospheric data collected over semiarid rangelands

Remotely sensed data in the visible, near‐infrared, and thermal‐infrared wave bands were collected from a low‐flying aircraft during the Monsoon '90 field experiment. Monsoon '90 was a multidisciplinary experiment conducted in a semiarid watershed. It had as one of its objectives the quantification of hydrometeorological fluxes during the “monsoon” or wet season. The remote sensing observations along with micrometeprological and atmospheric boundary layer (ABL) data were used to compute the surface energy balance over a range of spatial scales. The procedure involved averaging multiple pixels along transects flown over the meteorological and flux (METFLUX) stations. Average values of the spectral reflectance and thermal‐infrared temperatures were computed for pixels of order 10−1 to 101 km in length and were used with atmospheric data for evaluating net radiation (Rn), soil heat flux (G), and sensible (H) and latent (LE) heat fluxes at these same length scales. The model employs a single‐layer resistance approach for estimating H that requires wind speed and air temperature in the ABL and a remotely sensed surface temperature. The values of Rn and G are estimated from remote sensing information together with near‐surface observations of air temperature, relative humidity, and solar radiation. Finally, LE is solved as the residual term in the surface energy balance equation. Model calculations were compared to measurements from the METFLUX network for three days having different environmental conditions. Average percent differences for the three days between model and the METFLUX estimates of the local fluxes were about 5% for Rn, 20% for G and H, and 15% for LE. Larger differences occurred during partly cloudy conditions because of errors in interpreting the remote sensing data and the higher spatial and temporal variation in the energy fluxes. Minor variations in modeled energy fluxes were observed when the pixel size representing the remote sensing inputs changed from 0.2 to 2 km. Regional scale estimates of the surface energy balance using bulk ABL properties for the model parameters and input variables and the 10‐km pixel data differed from the METFLUX network averages by about 4% for Rn, 10% for G and H, and 15% for LE. Model sensitivity in calculating the turbulent fluxes H and LE to possible variations in key model parameters (i.e., the roughness lengths for heat and momentum) was found to be fairly significant. Therefore the reliability of the methods for estimating key model parameters and potential errors needs further testing over different ecosystems and environmental conditions.

Local energy flux estimates for unstable conditions using variance data in semiarid rangelands

A network of meteorological stations was installed during the Monsoon '90 field campaign in the Walnut Gulch experimental watershed. The study area has a fairly complex surface. The vegetation cover is heterogeneous and sparse, and the terrain is mildly hilly, but dissected by ephemeral channels. Besides measurement of some of the standard weather data such as wind speed, air temperature, and solar radiation, these sites also contained instruments for estimating the local surface energy balance. The approach utilized measurements of net radiation (Rn), soil heat flux (G) and Monin‐Obukhov similarity theory applied to first‐ and second‐order turbulent statistics of wind speed and temperature for determining the sensible heat flux (H). The latent heat flux (LE) was solved as a residual in the surface energy balance equation, namely, LE = −(Rn + G + H). This procedure (VAR‐RESID) for estimating the energy fluxes satisfied monetary constraints and the requirement for low maintenance and continued operation through the harsh environmental conditions experienced in semiarid regions. Comparison of energy fluxes using this approach with more traditional eddy correlation techniques showed differences were within 20% under unstable conditions. Similar variability in flux estimates over the study area was present in the eddy correlation data. Hence, estimates of H and LE using the VAR‐RESID approach under unstable conditions were considered satisfactory. Also, with second‐order statistics of vertical velocity collected at several sites, the local momentum roughness length was estimated. This is an important parameter used in modeling the turbulent transfer of momentum and sensible heat fluxes across the surface‐atmosphere interface.

Is large-scale inverse modelling of unsaturated flow with areal average evaporation and surface soil moisture as estimated from remote sensing feasible?

The potentiality of combining large-scale inverse modelling of unsaturated flow with remote sensing determination of areal evaporation and areal surface moisture is assessed. Regional latent and sensible heat fluxes are estimated indirectly using remotely sensed measurements by parameterizing the surface energy balance equation. An example of evapotranspiration mapping from northern and central Egypt is presented. The inverse problem is formulated with respect to the type of information available. Two examples of estimation of soil hydraulic properties by the dynamic one-dimensional soil-water-vegetation model SWATRE are given: one refers to a classical lysimeter scale and another one to a catchment scale. It is concluded that small-scale soil physics may describe large-scale hydrological behaviour adequately, and that the effective hydraulic parameters concerned may be derived by an inverse modelling approach. Remotely sensed data on surface reflectance, surface temperature and soil moisture content derived from multifrequency microwave techniques provide a useful data set on the mesoscale. The inverse modelling approach presented combined with a meso-scale data set on evaporation and surface soil moisture, considerable potentialities arise to determine effective meso-scale hydraulic properties.

A Comparative Analysis of Two Land Surface Heterogeneity Representations

Two contrasting representations of land surface variability used in general circulation models (GCMs) are compared through an analysis of their corresponding surface energy balance equations. In one representation (the 'mixture' approach), different vegetation types are assumed to be homogeneously mixed over a grid square, so that the GCM atmosphere sees near-surface conditions pertaining to the mixture only. In the second representation (the 'mosaic' approach), different vegetation types are viewed as separate 'tiles' of a grid-square 'mosaic', and each tile interacts with the atmosphere independently. The mosaic approach is computationally simpler and in many ways more flexible than the mixture approach. Analytical solutions to the linearized energy balance equations and numerical solutions to the nonlinear equations both demonstrate that the mixture strategy, when applied to two coexisting vegetation types that differ only in canopy transpiration resistance, promotes both total turbulent flux and latent heat flux relative to the mosaic strategy. The effective differences between the strategies, however, are small over a wide range of conditions. In particular, the strategies are effectively equivalent when the transpiration resistances of the different vegetation types are of the same order of magnitude.

A Numerical Model for Prediction of Road Temperature and Ice

Abstract A numerical model for the prediction of road temperature and ice has been tested on data from a Danish road station. The model is based on the solution of the equation of heat conduction in the ground and the surface energy-balance equation. Sensitivity experiments have been carried out in order to assess the relative importance of the various active processes. Large model sensitivity has been found to the specification of atmospheric input data. It is important to specify a realistic temperature and cloud structure in the lower part of the atmosphere. The best results were obtained with a detailed temperature and humidity analysis using significant points in the applied radiosonde data. Some further improvement was obtained with a simple scheme capable of adjusting the initial atmospheric temperature profile for analysis bias. The results indicate that the model can be used for high-quality road-temperature forecasts up to a range of at least 3 h. This requires a coupling of the model to a reali...

Satellite remote sensing of surface energy balance: Success, failures, and unresolved issues in FIFE

The FIFE staff science group, consisting of the authors, developed and evaluated process models relating surface energy and mass flux, that is, surface rates, to boundary layer and surface biophysical characteristics, that is, surface states. In addition, we developed and evaluated remote sensing algorithms for inferring surface state characteristics. In this paper we report the results of our efforts. We also look in detail at the sensor and satellite platform requirements (spatial resolution and orbital requirements) as driven by surface energy balance dynamics and spatial variability. We examine also the scale invariance of the process models and remote sensing algorithms, that is, to what degree do the remotely sensed parameters and energy balance relations translate from the patch level where they were developed to the mesoscale level where they are required? Finally, we examine the atmospheric correction and calibration issues involved in extending the remotely sensed observations within a season and between years. From these investigations we conclude that (1) existing formulations for the radiation balance and latent heat components of the surface energy balance equation are valid at the patch level. (2) Many of the surface physiological characteristics that parameterize these formulations can be estimated using satellite remote sensing at both local and regional scales; a few important ones cannot. (3) The mathematical structures relating radiation and surface energy flux to remote sensing parameters are, for the most part, scale invariant over the First International Satellite Land Surface Climatology Project (ISLSCP) Field Experiment (FIFE) study area. The conditions for scale invariance are derived. (4) The precision of satellite remote sensing estimates of surface reflectance, calibrated and corrected for atmospheric effects, is no worse than about 1% absolute. The errors may actually be smaller, but an upper bound of 1% results from sampling variance caused by differences among the satellite and ground sensors in spatial resolution, atmospheric effects, and calibration. (5) Afternoon cumulus in the study area required both the Landsat and the SPOT satellites for monitoring of the vegetation dynamics. This result implies the need for multiple polar orbiters, or geosynchronous satellites in an operational implementation. We found that canopy Fpar, the fraction of incident photosynthetically active radiation absorbed by a canopy, can be estimated with an error of about 10% using remote sensing, provided that regional variability in the reflectance of the canopy substrate is dealt with properly. We also found that spectral vegetation indices (VIs) respond primarily to the photosynthetically active radiation absorbed by the live or green component of the canopy as opposed to its necrotic or dead vegetation. This is of critical importance since radiation absorption by the live part of the canopy is the rate‐limiting process for photosynthesis and other key process rates such as evaporation. We found for the FIFE study area the surface moisture content at O to 10 cm to be another key rate‐limiting variable in photosynthesis and evaporation. At gravimetric soil moisture levels below 20%, photosynthesis and evaporation were strongly attenuated. Only microwave sensors have shown potential for satellite remote sensing of soil moisture and only in the top few centimeters. Hydrological models may also play a critical role in monitoring root zone soil moisture levels, but additional research is needed. From our review of the research of others in FIFE we conclude that downwelling shortwave radiation and surface albedo are also amenable to remote sensing. Unfortunately, from our research we also found that the remote estimation of surface temperature to useful accuracies is problematical; consequently, the use of thermal infrared measurements to infer sensible heat flux is probably not feasible to acceptable accuracies.

Extreme Maximum Land Surface Temperatures

Abstract There are numerous reports in the literature of observations of land surface temperatures. Some of these, almost all made in situ, reveal maximum values in the 50°–70°C range, with a few, made in desert regions, near 80°C. Consideration of a simplified form of the surface energy balance equation, utilizing likely upper values of absorbed shortwave flux (≈1000 W m−2) and screen air temperature (≈55°C), that surface temperatures in the vicinity of 90°–100°C may occur for dry, darkish soils of low thermal conductivity (≈0.1–0.2 W m−1 K−1). Numerical simulations confirm this and suggest that temperature gradients in the first few centimeters of soil may reach 0.5°–1°C mm−1 under these extreme conditions. The study bears upon the intrinsic interest of identifying extreme maximum temperatures and yields interesting information regarding the comfort zone of animals (including man).

Application of a mixed-layer model to bare soil surfaces

A model that couples the surface energy balance equation, a surface hydraulic resistance equation, and the force-restore soil temperature model to a mixed-layer model of the planetary boundary layer is described. The mixed layer is separated from the soil by a relatively thin surface layer and is overlain by a stable free atmosphere with prescribed profiles of potential temperature and water vapour density. The model is in reasonably good agreement with daytime micrometeorological measurements made at a wet bare site at Agassiz, British Columbia, and a desert site at Pampa de La Joya, Peru. The sensitivity of the mixed-layer model to conditions in the free atmosphere, to the parameters describing the growth of the mixed layer, and to surface roughness lengths, surface hydraulic resistance, and windspeed is examined.

Eddy Correlation Systems for Measuring EVAPOTRANSPIRATION

ABSTRACT A portable eddy correlation system was used to make direct, real-time mfeasurements of evapotranspiration over irrigated alfalfa. T^e surface energy balance equation was used to evaluate system performance, with the closure ratio defined as the ratio of the sum of latent and sensible heat fluxes to the sum of net radiation and soil heat flux. For six 24-hour periods, the mean uncorrected closure ratio was 0.85. After corrections were made for sensor separation, the mean closure ratio improved to 0.95. Measurements were made during several other periods, however, sensor malfunctions resulted in erroneous data during these periods. Care was required in deploying and maintaining the instruments, but the system proved to be a viable alternative for making real-time evapotranspiration measurements with portable equipment. KEYWORDS. Evapotranspiration, Eddy correlation. Irrigation, Measurement, Sensors.

Hourly ET Model Calibration with Eddy Flux and Energy Balance Data

The Penman equation for estimating hourly evapotranspiration (ET) of an alfalfa reference crop was calibrated for both daytime and nighttime conditions. Hourly net radiation, sensible heat flux, and soil heat flux were measured in the field for 16 24‐hr periods, and evaporative flux was determined as the residual of the surface energy balance equation. The sensible heat flux measurements were made using a portable eddy correlation system that included a sonic anemometer and a fine‐wire thermocouple. Following calibration, the hourly Penman model was applied to independent weather data from two growing seasons. Since only conventional weather parameters were measured during these two seasons, empirical equations were first developed to relate net radiation to solar radiation, and soil heat flux to solar radiation and air temperature. The resulting hourly ET estimates were summed over 2–4 day intervals and compared to ET data obtained from soil water balance measurements. Good agreement was found between es...

Soil heat and water flow with a partial surface mulch

A computer model using the alternating direction implicit (ADI) finite difference method to study two‐dimensional coupled soil heat and water flow with a partial surface mulch cover is developed. A new, simplified computational procedure, which has only tridiagonal matrix problems, for the ADI method is introduced. The model uses a soil surface energy balance equation to determine soil surface boundary conditions for both heat and water flow. The inputs required for the computer simulations are weather data, soil thermal and hydraulic properties, and mulch data. Numerical experiments are performed to examine the effects of soil type, mulch width, and weather conditions on soil heat and water movement. For continuous evaporation and drainage, 10‐day simulations were performed for each combination of clay, loam, and sand soil and fractions of mulch cover of 0, 0.5, 0.8, and 1.0 of the row interval width. For repetitive evaporation and infiltration, 15‐day simulations were performed. The mulch cover greatly reduces evaporation loss and the amplitude of daily soil temperature, water content, and pressure head variations. Large spatial variations in temperature and soil water content are predicted near the interface of mulch and bare soil surface. The soil hydraulic properties have important roles in controlling soil surface water content. The present model reasonably describes the soil thermal and hydrologic environments and thus can be applied successfully in soil science and groundwater hydrology and can be extended to related disciplines.

On solving the surface energy balance equation for surface temperature

Surface conditions are often assumed to be either “wet” or “dry” when applying the surface energy balance equation (SEBE) in biophysical studies. These somewhat restrictive assumptions facilitate linearization of the highly non-linear SEBE and permit easy solution of the equation. The linearization techniques and the errors introduced by not accounting for the actual degree of surface wetness, are discussed. An algorithm which employs Newton's iterative method for solving the non-linearized SEBE is offered as an alternative method. It is shown that Newton's method is capable of dealing with the general form of the SEBE which accounts for any degree of surface wetness and that with few iterations one can obtain surface temperature to any desired degree of accuracy.

Estimation of regional evapotranspiration of arable crops from thermal infrared images

Abstract By combining the surface energy balance equation with the vertical transport equations for latent and sensible heat, crop temperatures can, in principle, be transformed into instantaneous evapotranspiration values. To obtain 24 hour values the TERGRA model of Soer can be applied. In the method of Jackson et al. midday surface-air temperature differences are linearly related to 24 hour evapotranspiration and net radiation values. To estimate the slope of this relationship a crop-dependent analytical expression has been derived by Seguin and Itier. The present authors propose a modification of the method of Jackson by relating the actual crop temperatures to the temperature of the same but potentially transpiring crop. The net radiation term is replaced by the potential evapotranspiration of that crop. This means that the interpretation of heat images for each separate crop would produce a different linear relationship. From results obtained with the TERGRA model the slope of the linear relationshi...

A Sensitivity Analysis of a Numerical Model for Estimating Evapotranspiration

A simulation approach has been used to study the sensitivity of evaporation, estimated with an energy and moisture balance model, to the meteorological data used to drive the model. The numerical model solves the surface energy balance equation. Daily evaporation is calculated by integrating the instantaneous fluxes. A Monte Carlo method is used to apply random errors to the meteorological data, and constant biases are also applied. This was done for both bare and wheat fields. Previous sensitivity studies have used analytical methods, ignoring the interaction of the meteorological measurements, their biases, and the feedback mechanisms which couple the energy and moisture fluxes. The method described here removes these restrictions and does not require linearity and differentiability in the evaporation estimation technique. The numerical method was shown to produce results generally similar to those expected analytically for random errors under near‐potential conditions. Measurement biases produced larger errors in evaporation than random errors. The method will be applicable for dry conditions, where an analytical approach is not feasible.

Delineation of Cold-Prone Areas Using Nighttime SMS/GOES Thermal Data: Effects of Soils and Water

Infrared digital data from geostationary satellites were used to demonstrate the usefulness of remotely sensed surface temperature data to delineate microscale and mesoscale climates. Nocturnal winter data (December-February) from 1976–77 to 1978–79 over Florida revealed noticeable contrasts in surface temperature patterns. Colder areas were associated with low soil moisture content in the upper layers of excessively-drained and well-drained sandy soils, whereas warmer areas were associated with bodies of water, wetlands, or poorly drained soils. An unexpected surface temperature pattern for one night where the north-central Florida climatic zone was colder than the north Florida climatic zone was found to be caused by differences in antecedent frontal rainfall. Differences in surface radiant energy fluxes over these two areas at 0200 EST 20 December 1977, based on average satellite-sensed surface temperatures, were compared with differences in soil heat fluxes that were computed from 1.5 m climatological temperatures and soil thermal properties by use of a simplified surface energy balance equation. The difference in computed soil heat fluxes was in reasonable agreement with the difference in radiant energy fluxes from the surface of the two areas. It was therefore concluded that this method could be used to compute differences in thermal inertia of the surface layer of different areas based on satellite and climatological temperature data.

The sensitivity of response of climatic characteristics in a two-level general circulation model to small changes in solar radiation

A two-level, quasi-geostrophic, β-plane, general circulation model is developed, incorporating a time-dependent surface energy balance equation and a time-dependent heating function at the 500 mb level, with an associated feedback relationship. This system enables the surface temperature distribution to be evaluated as a function of time in the model, and so allows an associated variable spatial distribution of surface albedo to be carried in the model, including a simulated “snow and ice” edge. The effect on the model of successive small changes in solar radiation (of 1/2% up to a total of 3%) are then studied by carrying out numerical experiments over long time periods, these being sufficiently long (involving a total time of integration of 1800 model days) to produce oscillations in model heating and albedo distributions about asymptotic mean values. The successive latitudinal positions of the, zonally averaged, “snow and ice” edge agree approximately with those calculated by Gordon and Davies (1974) using a modified form of the statical energy balance method of Budyko (1969). However, the experiments also showed that the greater the reduction made in solar radiation the greater was the ensuing amplitude of spatial movement of the associated albedo distribution, implying a strong tendency towards instability of the simulated edge as the reduction approached a value of 3%. DOI: 10.1111/j.2153-3490.1977.tb00761.x

Potential evaporation: The combination concept and its experimental verification

Using a combination of a surface energy balance equation and an approximate expression of water vapor and sensible heat transfer, an equation is formulated relating potential evaporation for net radiation, ambient air properties, and surface roughness. As an improvement over the earlier Penman version, the proposed model contains no empirical constants or functions. Tests of the model in Phoenix, Arizona, using open water, wet bare soil, and well watered alfalfa, show excellent agreement of calculated and measured values on an hourly and daily basis under a variety of circumstances. Test conditions typically included advection of sensible heat to the evaporating surface in a large proportion to the latent heat flux, as well as high values of radiant flux, ambient temperatures, and vapor pressure deficits. The use of daily average values for the weather variables in the model, rather than hourly data, did not give appreciably different results or conclusions on a series of mostly clear days, suggesting that the combination model is not only accurate but also practical and generally applicable. (Key words: Evaporation; evapotranspiration; meteorology)

Energy balance components of evaporating surfaces in arid lands

The components of the surface energy balance equation Rn + S + (S or W) + LE + A = 0 were determined during April and May 1961 in experiments conducted over an extended wet, bare soil surface and over an extended area of shallow water in the vicinity of Phoenix, Arizona. Evaporative flux (LE) measurements were found from sensitive weighing lysimeters. Net radiation (Rn) was measured with miniature net radiometers. Soil heat flux (S) was measured with heat-flow transducers. The change in energy storage of the layer of soil (S′) or water (W) above the heat-flow transducer was computed using direct measurements of soil or water temperature. The sensible heat flux into the air (A) was determined by solving the energy balance equation. The results of triplicate measurements made every 15 minutes for nine consecutive days indicate that the daily totals of the sensible heat flux to the air were generally negative, that is, away from the surface. The rate of evaporation was larger from a wet soil surface than from a free water surface. On days of similar solar radiation, the evaporative flux tended to be correlated with wind speed.