Hydrometeorological models are often evaluated and optimized on the basis of micrometeorological measurements. However, it has been known for more than three decades that surface measurements of sensible and latent heat energy (LE) are systematically underestimated. We studied this problem using six years of eddy-correlation measurements for four fields (corn, soybean, and prairie) in central Iowa, USA. We recorded major components of the energy equation (i.e. net radiation, sensible heat flux, LE, and soil heat flux, photosynthesis), and indirectly estimated most of the minor components of energy balance (namely storage in the soil, canopy and air). Storage in the canopy was related to leaf area index (LAI) acquired from Moderate Resolution Imaging Spectrometer (MODIS). In this paper, a diagnostic approach is investigated where systematic error is identified first. Three dimensional (3D) plots of the residual of energy equation vs. potential variables indicated the imbalance was largest mainly during the cold non-growing season when the soil was dry. Correlations between energy balance residual (EBR) and energy components showed that soil storage was not precisely estimated. Finally, an a-posteriori analysis (constrained linear multiple regression (CMLR)) was conducted to quantify the contribution of major/minor components of the energy equation towards EBR. The result highlights that the contribution of pertinent components of energy to EBR is mainly controlled by prevailing monthly hydrometeorological conditions; however, precise quantification of causes of imbalance is site-specific. A comparison between the a-posteriori analysis technique and the Bowen-ratio method demonstrates that the Bowen-ratio basically presumes a higher level of underestimation in LE. The results obtained in this study suggest that a-posteriori analysis may offer a superior methodology to correct measured eddy-correlation measurements. Furthermore, the overall trends in the correction of LE measurements suggest that there is a potential for rough monthly corrections of LE, irrespective of the type of crop.
Generally, researchers evaluate and optimize hydrological models on the basis of on-site micrometeorological measurements. As with all measurements, these are subject to uncertainty and what appears to be a systematic bias. We focus on the lack of closure in the energy equation (Equation (1)) at the surface―usually referred to as the surface energy balance closure (EBC) problem―which researches have noted for at least three decades:
where Rn is net radiation, LE denotes latent heat flux, Hs represents sensible heat flux, and G is ground heat flux, all normally represented in [W∙m−2] [
The practical applications of precise estimation of ET include irrigation scheduling, water conservation, global warming, and flood prediction, etc. [
Higgins [
This work supports the Iowa Flood Center's (http://iowafloodcenter.org/) development of a flood warning system where spatially-resolved daily ET over Iowa is required by the model. Analysis of land cover Cropland Data Layer (CDL) maps provided by National Agricultural Statistics Service (NASS) shows that 80% of Iowa is covered by corn, soybeans, and prairie. These sites were as being typical of Iowa. Additionally, these sites are long term sites maintained by the USDA National Laboratory for Agriculture and Environment (NLAE) with high-quality, well-maintained equipment. NLAE, Ames, Iowa [
The data consisted of105 measured or derived variables (eddy-covariance fluxes, radiative fluxes, hydrometeorological data, covariance fluxes, soil properties, etc.). We computed turbulent fluxes of Hs, LE and momentum from the micrometeorological sensors using an eddy-covariance system operating at 20 Hz.
Site # | Site ID | Latitude/Longitude/Altitude | Land Cover |
---|---|---|---|
1 | Brooks10 | 41˚58''29.7696"N 93˚41''26.1024"W + 314 | Corn/Soybeans |
2 | Brooks11 | 41˚58''28.1928"N 93˚41''37.3704"W + 315 | Corn/Soybeans |
3 | BeenofIowa | 41˚59''01.9860"N 93˚40''56.7480"W + 315 | Corn/Soybeans |
4 | NSPprairie | 41˚33''31.0356"N 93˚17''34.3104"W + 279 | Restored Prairie |
Instrument | Mfg./Model | Variable (s) | Heightb |
---|---|---|---|
3D sonic anemometer | Campbell Scientific CSAT3 | U, v, w, Tv, LE, Hs | 1.8 - 5.2 m |
Infrared gas analyzer | LI-COR 7500 | CO2, H2O | 0.84 - 5 m |
HMP45C | PRT | Ta | 1.55 - 5.3 m |
Humidity probe | Honeywell HIH-4602C | RH | 1.55 - 5.3 m |
Infrared sensor | IRPT-P3, Apogee Inc. | Ts, Tc | 0.84 - 5 m |
Net radiometer | K & Z CM-21 | Rn | 1.4 - 6.1 m |
Bucket | - | Rain | 10 cm |
SHFP | HFT-3.1 | SHFa | 6, 8, 10 cm |
Soil thermocouple | Campbell Scientific 107-L | SoilTCa | 2, 4, 6 cm |
Soil moisture probe | Hydra 50 Hz | Hydra_Va | 5 cm |
au, v, and w are wind components; LE, Hs and SHF represent latent, sensible, and soil heat flux, respectively; Ta, Ts, and Tc denote air, surface, and above-canopy temperature, in order; RH stands for relative humidity; Rn is net radiation; SoilTC and Hydra_V represent soil temperature and probe’s voltage. bHeights varied typically year-by-year, site-by-site, and in summer/winter period, and are above-ground measurements. cDenotes measurements of same variable at different locations.
the other between the rows. The elevation of the SHFPs changed each year for different fields. We buried four soil thermocouples: two above each of the SHFPs were co-located and their elevation varied annually at 2, 4, and 6 cm below ground. Infrared Gas Analyzers (IRGAs) were open path sensors. The temperature-humidity sensors contained thin-film platinum resistance thermometers thermally attached to a capacitive relative humidity (RH) sensor.
Raw measurements from instruments may contain erroneous data and need to be refined in a secondary process before application. We imported the data into MATLAB®, and eliminated outliers and suspicious values based on our suggested lower/upper thresholds specific for each variable, recorded in
We visually checked the data, and removed corrupted records by means of MATLAB graphically interactive functions. In some periods, soil heat flux at one field had an abnormal reverse pattern. We believe that the operator incorrectly wired the plate. The RH during some periods was not recorded; the data was recovered from vapor density and air temperature [
In this section, first attempts are made to estimate the contribution of minor components of energy balance equation. Some of the components are directly computed from the field measurements, and the rest (i.e. heat storage in the canopy, and advection) are indirectly estimated. Then, we try to pinpoint and measure any systematic error according to the scatterplots of the residual of energy vs. independent variables. Further, this helps to identify any imprecise estimation of energy balance equation components on the basis of any visible trend. The next step is devoted to pointing out the location and reason of high residual based on three-dimensional (3D) plots of residual of energy equation vs. potential covariates. Finally, an a-posteriori analysis (constrained linear multiple regression (CMLR)) will be performed to bring balance to the energy equation and quantify the contribution of major/minor components of the equation.
Variable | Variable | Unit | Threshold | Filtering | |
---|---|---|---|---|---|
Dataset Name | Description | Low-High | m, n | Conditions | |
CO2_wpl | Photosynthesis | W/m2 | (−35, 18) | - | - |
Conductivity | Conductivity | S/m | (0.001, 10) | - | - |
Hs | Sensible heat flux | W/m2 | (−100, 500) | 5, 5 | Va > 3F & |V| > 60 |
Hydra_Soil | Soil Probe temp. | ˚C | (−20, 50) | - | - |
Hydra_SWC | Soil water content | m3/m3 | (0.001, 1) | - | |diff(V)| > 0.2 |
Hydra_V* | Probe voltage | mV | [0, 2500) | - | - |
IRT_can_Avg | Canopy temperature | ˚C | (−30, 60) | 5, 5 | |V-F| > 10 |
LE_wpl | Latent heat (with Webb et al. term) | W/m2 | [0, 500) | 19, 19 | V > 3F & V > 15 |
press_Avg | Air pressure | kPa | [0, 200) | - | - |
rh_hmp_Avg | RH above canopy | - | [0, 1) | - | - |
Rn_Total_T_Cor_Avg | Net radiation (temp-corrected) | W/m2 | (−100, 1200) | - | - |
SHF*_Avg | Soil heat flux at plate | W/m2 | (−60, 200) | - | - |
SoilTC*_Avg | Soil temperature | ˚C | (−20, 50) | - | - |
Sa | Heat storage in air | W/m2 | (−10, 10) | - | - |
Sc | Canopy heat storage | W/m2 | (−40, 40) | 11, 5 | |V-F| > 50 |
Sg | Heat storage in soil | W/m2 | (−500, 500) | 3, 5 | |V-F| > 80 |
t_hmp_Avg | HMP45C Temp. above canopy | ˚C | [−50, 60) | - | - |
u_star | Friction velocity | m/s | [0, 2.5) | 10, 1 | |V-F| > 0.2 |
wfv1 | Soil water content | m3/m3 | (0.001, 1) | - | |diff(V)| > 0.2 |
wnd_dir_com | Compass wind dir. | Deg. | [0, 360) | - | - |
wnd_spd | Wind velocity | m/s | [0, 100) | - | |diff(V)| > 0.2 |
aV stands for variable and F represent the response of filter function. *Denotes different measurements of same variable at different locations.
There are three primary causes for energy imbalance: measurement errors, the nonidentical elevations of these measurements, and the elimination of “insignificant” components contributing to the energy equation [
The first type of error is attributed to measurement errors. The expected measurement errors associated with the instrumentation in this study include: the accuracy of the CSAT3 anemometer for Hs and LE, the K&Z CMP 21 Pyranometer error, IRPT-P3 infrared sensor measurement errors, soil temperature measurement errors, air temperature measurements errors, and CO2 concentration measurement errors. The accuracy of the CSAT3 anemometer for Hs and LE is 10% or 10 W/m2, and 10% or 20 W/m2, respectively [
The second type of error refers to the fact that the measurements of the main energy components (i.e. Rn, Hs, LE, & G) are not made at the same location (see
The third type of error comes from ignoring what many consider “inconsequential” terms in the energy balance equation, thus relying upon an inaccurate equation (i.e. Equation (1)). Terms that researchers generally presumed negligible may turn out to be significant under certain circumstances, such as storage terms [
where S represents heat storage in the canopy, and F denotes photosynthesis where CO2 flux is used as an indicator. SHF stands for Soil Heat Flux at the plate; given the fact that plates are buried in the ground, some energy is always stored between the plate and surface (Sg), and ground heat flux (G) will be calculated from algebraic summation of SHF and Sg. A is the advection term, ε represents systematic measurement errors, and c is other terms which include mismatched measurement footprints, freeze/thaw in a snowpack, and soil water transport, etc. [
In order to better analyze contributing factors to the energy imbalance, we estimated the non-measured components of Equation (2). The first component is the storage term, partitioned into three components: heat storage in the soil (Sg), the air (Sa), and the canopy (Sc). The first part of storage term, Sg, heat storage in the soil has turned out to be a significant factor in the accurate estimation of ground heat flux [
where ρsoil and ρw are soil bulk and water density, respectively; Csoil and Cw are, in order, specific heat capacity of mineral soil and water; ΔTsoil denotes temperature difference between at-surface and top plate; Δt is time step; and Δz is the depth of SHF plate [
The second part of storage occurs in the canopy. We estimated the rate change in the enthalpy of the canopy within each 15-minute time interval (Sc) from temperature gradient and available water/biomass:
where Tc represents canopy temperature, and Cb is specific heat capacity of biomass in the plant. The nomenclature mw and mb represent water and biomass content in the canopy, respectively, and can be quantified by plant destruction. In the absence of such destruction, we related the aforementioned parameters to Leaf Area Index (LAI) on the basis of the curves presented by Meyers and Hollinger [
where the values of parameters are suggested in
plant | LAImax | mwmax [kg∙m−2] | mbmax [kg∙m−2] |
---|---|---|---|
Corn | 4.5 | 6.8 | 2.5 |
Soy | 3.2 | 2.4 | 0.8 |
prairie | 2 | 2 | 0.5 |
In addition to energy storage in the soil and canopy, heat energy is stored in the air. We quantified the heat storage in the air (Sa) in the sense that we took into account the effect of specific humidity levels [
In the equations above, ρm and ρv represent moist air and water vapor density, respectively; Cm, Cp and Cv denote, in order, specific heat capacity of moist air, air, and water vapor at constant pressure; Ta is air temperature; and hEC is the height of the eddy covariance instrument below which the energy is stored in the air.
The next term in Equation (2) is photosynthesis, F. We converted CO2 fluxes to photosynthesis by Lp, thermal conversion factor for fixation of CO2 [
Since quantification of advection requires numerous instruments, Higgins [
where f is an unknown function of wind direction and atmospheric stability, z/L. CA represents adjusting factor, and z denotes measurement height. The Monin-Obukhov length is generally used as an indicator of atmosphere stability (L < 0, L = 0, and L > 0, respectively for unstable, neutral, and stable phase), and can be represented as a function of friction velocity, latent, and sensible heat flux:
where U* is fiction velocity; ρa denotes density of air; and g, κ, and Le represents acceleration due to gravity, Von-Karman constant, and latent heat of vaporization, respectively [
where Cij are unknown coefficients.
Subplot (k) suggests that Sg is not precisely estimated. Although this may be due to the assumption of a linear soil temperature profile, estimation of Sg using an exponential profile [
To better pinpoint the location of the significant residuals, we generated 3-dimensional (3D) plots of residual vs. potential covariates.
We conducted an a-posteriori analysis to identify the individual contributions to the residual. This type of a- posteriori analysis, suggested by Higgins [
where a total of 17 coefficients must be determined. Higgins recommends that an a-posteriori analysis be conducted separately for different stability conditions [
As our study shows, Rn is overestimated during the growing season. Even though there could be at most 4% uncertainty in Rn, no arguments can be found in the literature to prove that the net radiation is overestimated [
The micrometeorological data explored in this paper are meant to be exploited for evaluation of an evapotranspiration model implemented by the authors, and hence, precise quantification of latent heat flux is the primary motivation of this study. Therefore, in order to evaluate the response of each site against an a-posteriori
analysis, we performed the technique separately for each site, each year, and vectors of balancing coefficients, for a total of 18 parameters (shown in
As previously mentioned, the Monin-Obukhov length, L, is a measure of atmospheric stability (L< 0, L = 0, and L > 0 represent stable, neutral, and unstable phase, respectively). The dimensionless stability parameter, z/L, is also widely used in parallel with Monin-Obukhov length, where z is the height of hydrometeorological measurements. The term z/L is zero at statically neutral conditions, and it is positive (negative) in a typical range of 1 to 5 (−5 to −1) for stable (unstable) stratification [
One of the most serious concerns of energy imbalance lies in latent heat flux measurements. Latent heat flux plays a key role in mesoscale models, and its precise quantification has been a challenging issue for decades [
analysis approach has increased LE more than the Bowen ratio method. Unexpectedly, the upper bound of the Bowen ratio method is in a linear relationship with the a-posteriori analysis technique, implying that the Bowen- ratio method, at its highest level, can adjust latent heat flux up to 2.6 times when compared with the a-posteriori analysis. In consideration of the range of LE balancing coefficient obtained during evaporative season, this might suggest that the Bowen-ratio method [
In this paper, we attempted to identify and correct the root causes of lack of energy closure in three agricultural fields. We found that the energy equation suffered most from imbalance during the cold non-growing season. This might strongly be attributed to freeze/thaw in a snowpack, as confirmed by Hoffman et al. [
This work was accomplished under the grant support of Iowa Flood Center (IFC). We are grateful to the USDA National Laboratory for Agriculture and Environment, Ames, IA for providing the micrometeorological data. The MCD15A3 was retrieved from the online Data Pool, courtesy of the NASA EOSDIS Land Processes Distributed Active Archive Center (LP DAAC), USGS/Earth Resources Observation and Science (EROS) Center, Sioux Falls, South Dakota, https://lpdaac.usgs.gov/data_access/data_pool. We also express our appreciation to the anonymous reviewers for their constructive remarks.
Ali Varmaghani,William E. Eichinger,John H. Prueger, (2016) A Diagnostic Approach towards the Causes of Energy Balance Closure Problem. Open Journal of Modern Hydrology,06,101-114. doi: 10.4236/ojmh.2016.62009