Complementary Relationship Model Research Articles

Comment on “Rescaling the complementary relationship for land surface evaporation” by R. Crago et al.

AbstractThe generalized complementary relationship (GCR) model of Brutsaert (2015) has been widely applied to estimate land surface evapotranspiration (E) over Chinese eastern monsoon region, Loess Plateau and Australia. However, Crago et al. (2016, hereinafter C16) recently noted a deficiency in one of his boundary conditions and proposed a novel approach to improve it. The key of this approach is to determine the ratio (xmin) of the potential evapotranspiration (Epo) to the apparent potential evapotranspiration for an entirely dry surface (Epads) at which E tends to be vanishing. As seen, the physically reasonable range of xmin should be between 0 and 1. The present comment reports that the xmin in C16 may become invalid under conditions of relatively strong available energy but weak winds if Epads is calculated by the mass‐transfer‐based method, thereby causing unrealistic estimation of E. A more preferable way to determine Epads is still based on the traditional Penman‐based equation with consideration of the characteristics of dry air in which Epads occurs.

Applicability of three complementary relationship models for estimating actual evapotranspiration in urban area

Abstract The characteristics of evapotranspiration estimated by the complementary relationship actual evapotranspiration (CRAE), the advection-aridity (AA), and the modified advection-aridity (MAA) models were investigated in six pairs of rural and urban areas of Japan in order to evaluate the applicability of the three models the urban area. The main results are as follows: 1) The MAA model could apply to estimating the actual evapotranspiration in the urban area. 2) The actual evapotranspirations estimated by the three models were much less in the urban area than in the rural. 3) The difference among the estimated values of evapotranspiration in the urban areas was significant, depending on each model, while the difference among the values in the rural areas was relatively small. 4) All three models underestimated the actual evapotranspiration in the urban areas from humid surfaces where water and green spaces exist. 5) Each model could take the effect of urbanization into account.

Positive or negative correlation between actual and potential evaporation? Evaluating using a nonlinear complementary relationship model

Understanding whether a positive or negative correlation between actual (E) and potential (Ep) evaporation is of great importance in detecting changes of E from Ep. In this study, such correlation was evaluated via the linear regression slope (k) between E and Ep derived from a nonlinear complementary relationship model. k varies with the relative degree of variability in the radiation term (Erad) and aerodynamic term (Eaero) of Ep, and is further affected by water availability. The sign of k is always positive under conditions with high Erad variability but at the same time with low Eaero variability (commonly true on an hourly basis). Under conditions with high Eaero variability but at the same time with low Erad variability, the sign of k tends to change from negative to positive with more readily water availability. On a daily or annual basis, the sign of k would be related with water availability. Under water-limited conditions, the Eaero variability is more significant than the Erad variability, and negative k is expected. Under energy-limited conditions, the Erad variability is compared to or even much obvious than the Eaero variability, and positive k is expected. This implies a negative correlation between E and Ep under water-limited conditions but a positive correlation under energy-limited conditions on the daily or annual basis. The above analysis is confirmed in a grassland site in Northeast China at daily and half-hourly time scales. The correlation between annual E and Ep over China was evaluated using data of 690 meteorological stations from 1956 to 2005. The k values change from negative in arid regions to positive in humid regions. According to k and the decreasing trends in annual Ep, it is deduced that E increased for most stations in arid regions but decreased for most stations in humid regions.

Estimating high spatiotemporal resolution evapotranspiration over a winter wheat field using an IKONOS image based complementary relationship and Lysimeter observations

Mapping high spatiotemporal resolution evapotranspiration (ET) over large areas is important for water resources planning, precision irrigation and monitoring water use efficiency. However, both traditional field measurement and aerodynamic estimation mainly focus on obtaining local ET. Remote sensing observations usually can be used to retrieve instantaneous ET at a low spatial resolution over region or global scale. Therefore, using field measurements and high resolution image data to generate high spatiotemporal resolution ET is becoming an important research direction. In this study, the complementary relationship model (CR) was tested together with meteorological data to estimate actual ET, and the results were validated by the Lysimeter observation. Furthermore, CR model combined with high resolution IKONOS data was used to estimate instantaneous field scale ET that was then transferred to daily ET. The cumulative evapotranspiration (ET) of winter wheat during the reproductive period from March through June of 2011 was 469.12mm, essentially corresponding to the annual precipitation in the study area. The highest accuracy of estimating ET by CR model with remote sensing data was in May (R2=0.863, RMSE=0.103mm). The transferred daily ET by a self-preservation of evaporative fraction (EF) approach from the CR modeling instantaneous ET was consistent with The Lysimeter measurements for all four months, March through June, 2011 (R2=0.937, RMSE=0.668mm). The experimental results demonstrate that CR model can be used to accurately estimate actual ET with both meteorological data and high resolution remote sensing data at a regional scale.

Similarities and differences of two evapotranspiration models with routinely measured meteorological variables: application to a cropland and grassland in northeast China

Local actual evapotranspiration can be estimated with routinely measured meteorological variables using the Penman–Monteith model with surface resistance parameterized via the Katerji and Perrier approach (Agronomie 3(6):513–521, 1983; PM–KP model), or the nonlinear complementary relationship (CR) model proposed by Han et al. (Hydrol Process 26:3973–3981, 2012). A comparative study was carried out to evaluate the consistencies and differences of two models, as well as the performances of them for a cropland and grassland in northeast China. The departure of the actual evapotranspiration from the potential evaporation is described as a function of the ratio of the surface resistance to the aerodynamic resistance in the Penman–Monteith model, but the ratio of the aerodynamic term to the radiation term in the CR models. The two ratios are connected using a semi-empirical linear function by the Katerji and Perrier approach. The nonlinear CR model can be regarded as replacing the linear function by a power function after mathematical processing. On the other hand, the PM–KP model can be also considered as a CR-type model. On the daily basis at a maize cropland and degraded grassland in semiarid Northeast China, the nonlinear CR model with locally calibrated parameters performed better with data occupying all the growth stages, but the performances of the two models are similar during the early-, mid-, and late-season stages, respectively. On the half-hourly basis, the PM–KP model and the nonlinear CR model both performed well. It is deduced that on the daily basis the nonlinear CR model is more suitable for the cropland and grassland, but further comparisons are needed on the hourly basis.

Temporal-spatial analysis of farmland evapotranspiration based on complementary relationship model and IKONOS data

Temporal-spatial analysis of farmland evapotranspiration based on complementary relationship model and IKONOS data

A nonlinear function approach for the normalized complementary relationship evaporation model

AbstractA nonlinear function approach for the normalized complementary relationship evaporation model that is different from the methodology maintaining the symmetric complementary relationship with appropriate definitions of potential and wet‐environment evaporation is proposed and verified. This approach employs the definitions used in the advection‐aridity model, wherein the potential is estimated using the Penman equation. Normalized by Penman potential evaporation, the complementary relationship model is expressed as a function describing the relationship between the evaporation ratio (the ratio of the actual to the Penman potential evaporation) and the proportion of the radiation term in Penman potential evaporation. The new nonlinear function proposed in the current study is approximately equivalent to the advection‐aridity and the modified Granger models under conditions that are neither too wet nor too dry, but is more reasonable under arid and wet conditions. The new nonlinear function model performs well in estimating actual evaporation, as verified by the observed data from four sites under different land covers. Copyright © 2011 John Wiley & Sons, Ltd.

Spatial and temporal characteristics of actual evapotranspiration over Haihe River basin in China

Spatial and temporal characteristics of actual evapotranspiration over the Haihe River basin in China during 1960–2002 are estimated using the complementary relationship and the Thornthwaite water balance (WB) approaches. Firstly, the long-term water balance equation is used to validate and select the most suitable long-term average annual actual evapotranspiration equations for nine subbasins. Then, the most suitable method, the Pike equation, is used to calibrate parameters of the complementary relationship models and the WB model at each station. The results show that the advection aridity (AA) model more closely estimates actual evapotranspiration than does the Granger and Gray (GG) model especially considering the annual and summer evapotranspiration when compared with the WB model estimates. The results from the AA model and the WB model are then used to analyze spatial and temporal changing characteristics of the actual evapotranspiration over the basin. The analysis shows that the annual actual evapotranspirations during 1960–2002 exhibit similar decreasing trends in most parts of the Haihe River basin for the AA and WB models. Decreasing trends in annual precipitation and potential evapotranspiration, which directly affect water supply and the energy available for actual evapotranspiration respectively, jointly lead to the decrease in actual evapotranspiration in the basin. A weakening of the water cycle seems to have appeared, and as a consequence, the water supply capacity has been on the decrease, aggravating water shortage and restricting sustainable social and economic development in the region.

A complementary relationship evaporation model referring to the Granger model and the advection–aridity model

AbstractA complementary relationship evaporation model has been proposed and verified based on evaluations of the advection–aridity model and the Granger's complementary relationship model (Granger model) in dimensionless forms. Normalized by Penman potential evaporation, the Granger model and the advection–aridity model have been transformed into similar dimensionless forms. Evaporation ratio (ratio of actual evaporation to Penman potential evaporation) has been expressed as a function of dimensionless variable based on radiation and atmospheric conditions. Similar dimensionless variables for the different functions have been used in the two models. By referring to the dimensionless variable from the advection–aridity model and the function from the Granger model, a new model to estimate actual evaporation was proposed. The performance of the new model has been validated by the observed data from four sites under different land covers. The new model is an enhanced Granger model with better evaporation prediction over the aforementioned different land covers. It also offers more stable optimized parameters in a grassland site than the Granger model. The new model somewhat approximates the advection–aridity model under neither too wet nor too dry conditions, but without its system bias. Copyright © 2011 John Wiley & Sons, Ltd.

The spatio-temporal distribution of thermodynamic forces at the land-atmosphere interface in China

Correlation analysis and the complementary relationship model are used to indirectly measure and characterize the dynamic and thermodynamic properties at the land-atmosphere interface in China. Results show that thermodynamic forces driving the exchange fluxes of energy, water and carbon between the land surface and the overlying atmosphere are significantly enhanced along the mid-upper reaches of the Yangtze River basin around Sichuan Basin and the northern region of Heilongjiang. The thermodynamic forces exhibit a decreasing trend in southern Xinjiang and some regions of Yunnan. Low cloud cover was shown to be a significant factor leading to changes in thermodynamic properties at the land-atmosphere interface. Western Pacific Subtropical High (WPSH) and storm data provide strong evidence that a changing synoptic system is likely a principle factor causing the abnormal spatiotemporal distribution of thermodynamic forces over the land surface in China. This data also suggests that cyclical and quasi-cyclical fluctuations of low cloud cover in most regions of China are responsible for annual rainfall patterns. At the same time, NOAA-AVHRR satellite remote sensing data illustrates that changes to land surface characteristics may cause atypical spatiotemporal distributions of thermodynamic forces over the land surface. We show that thermodynamic forces are weakening in regions with increasing vegetation. However, where urbanization has decreased the quantity of vegetation, thermodynamic forces are rising. Finally, an increase in large-scale thermodynamic forces is associated with a reduction in low cloud cover due to changes in the synoptic system.

Impact of an unstressed canopy conductance on the Bouchet‐Morton complementary relationship

Indirect methods of quantifying evapotranspiration (λEa) are sought since regional estimations of λEa require prohibitive instrumentation or highly parameterized and data‐intensive land surface models (e.g., involving temporally and spatially varying soil moisture, soil hydraulic properties, and vegetation properties). Complementary relationship (CR) models, based on Bouchet's hypothesis, are one such method of estimating λEa from routinely measured meteorological variables. Bouchet's CR states that given a change in regional surface moisture availability (MA), changes in λEa are reflected in changes in potential evapotranspiration (λEp), such that λEa + λEp = 2λE0, where λE0 is an assumed equilibrium condition at which λEa = λEp = λE0 given sufficiently large MA. Whereas λEp conceptually includes a transpiration component, the treatment of vegetation in existing CR applications varies from neglecting it to indirectly accounting for it through recalibration of Penman's empirical wind function. We utilize the First International Land Surface Climatology Field Experiment (FIFE) data set to demonstrate that inclusion of a maximum (i.e., unstressed) canopy conductance (gc,max) in a Penman equation with stability‐corrected atmospheric conductance (i.e., replacing the Penman equation with an unstressed Penman–Monteith equation) significantly improves both CR convergence and symmetry. Inclusion of gc,max results in more accurate λEa estimates than are found with the Penman equation (using either Monin–Obukhov atmospheric conductance or using empirical wind functions in the literature). The proposed method also performs better than the 1992 advection‐aridity CR method, modified to include atmospheric stability effects, which attributes noncomplementarity to horizontal advection and corrects for it by adjusting λE0 by the magnitude of the potential sensible heat flux (∣Hp∣), found from the surface energy balance of the λEp calculation. In the proposed method a similar energy balance adjustment occurs naturally because the finite canopy conductance causes an increase of surface temperature and sensible heat flux in the λEp energy balance calculation. The proposed method is consistent with CR explanations that rely on feedbacks with the boundary layer vapor pressure deficit since the impact of such changes on both λEp and λEa would be modulated by stomatal conductance.

Should Bouchet's hypothesis be taken into account in rainfall‐runoff modelling? An assessment over 308 catchments

AbstractAn implementation of the complementary relationship hypothesis (Bouchet's hypothesis) for estimating regional evapotranspiration within two rainfall‐runoff models is proposed and evaluated in terms of streamflow simulation efficiency over a large sample of 308 catchments located in Australia, France and the USA. Complementary relationship models are attractive approaches to estimating actual evapotranspiration because they rely solely on climatic variables. They are even more interesting since they are supported by a conceptual description underlying the interactions between the evapotranspirating surface and the atmospheric boundary layer, which was highlighted by Bouchet (1963). However, these approaches appear to be in contradiction with the methods prevailing in rainfall‐runoff models, which compute actual evapotranspiration using soil moisture accounting procedures. The approach adopted in this article is to introduce the estimation of actual evapotranspiration provided by complementary relationship models (complementary relationship for areal evapotranspiration and advection aridity) into two rainfall‐runoff models. Results show that directly using the complementary relationship approach to estimate actual evapotranspiration does not give better results than the soil moisture accounting procedures. Finally, we discuss feedback mechanisms between potential evapotranspiration and soil water availability, and their possible impact on rainfall‐runoff modelling. Copyright © 2005 John Wiley & Sons, Ltd.

Evaluation of three complementary relationship evapotranspiration models by water balance approach to estimate actual regional evapotranspiration in different climatic regions

Three evapotranspiration models using the complementary relationship approach for estimating areal actual evapotranspiration were evaluated and compared in three study regions representing a large geographic and climatic diversity: NOPEX region in Central Sweden (cool temperate, humid), Baixi catchment in Eastern China (subtropical, humid), and the Potamos tou Pyrgou River catchment in Northwestern Cyprus (semiarid to arid). The models are the CRAE model of Morton, the advection–aridity (AA) model of Brutsaert and Stricker, and the GG model proposed by Granger and Gray using the concept of relative evapotranspiration (the ratio of actual to potential evapotranspiration). The calculation was made on a daily basis and comparison was made on monthly and annual bases. The study was performed in two steps: First, the three evapotranspiration models with their original parameter values were applied to the three regions in order to test their general applicability. Second, the parameter values were locally calibrated based on the water balance study. The results showed that (1) using the original parameter values all three complementary relationship models worked reasonably well for the temperate humid region, while the predictive power decreases in moving toward regions of increased soil moisture control, i.e. increased aridity. In such regions, the parameters need to be calibrated. (2) Using the locally calibrated parameter values all three models produced the annual values correctly. For the monthly values there was a time shift for the appearance of maximum monthly values between the evapotranspiration model estimations and water balance calculations, and the drier the region, the larger the difference. Further examination of the water balance components showed that while the actual evapotranspiration is controlled by several hydrometeorological factors in warmer and drier months the soil moisture is the dominating factor.