Available at: http://publications.ictp.it IC/2010/084

United Nations Educational, Scientific and Cultural Organization and

International Atomic Energy Agency

THE ABDUS SALAM INTERNATIONAL CENTRE FOR THEORETICAL PHYSICS

ESTIMATION OF SURFACE ENERGY FLUXES USING THE PENMAN MONTEITH METHOD IN A TROPICAL STATION

M.O. Adeniyi1 Department of Physics, University of Ibadan, Nigeria

and The Abdus Salam International Centre for Theoretical Physics, Trieste, Italy

and

T.A. Otunla2

Department of Physics, University of Ibadan, Nigeria.

Abstract

The Penman Monteith (PM) model was applied in the estimation of sensible and latent heat fluxes on Nigerian Micrometeorological Experiment (Nimex_1) field at Obafemi Awolowo University, Ile-Ife, Nigeria, so as to validate its usage by comparing with direct eddy covariance measured fluxes. The resulting fluxes from the PM model were comparable to the measured eddy covariance ones. The root mean squared error (RMSE) ranging from 17.63 to 22.11Wm-2 and 38.72 to 76.08 Wm-2 was obtained for sensible and latent fluxes, respectively. The coefficient of determination for sensible and latent heat fluxes ranged from 0.83 to 0.90 and 0.78 to 0.90, respectively, with trend lines at the origin. The PM model gave a better estimation of sensible heat flux than the latent heat flux. The PM method was found to be rugged with respect to the choice of values for parameters of the correction advective term Fw which requires the inclusion of the relative humidity of the ground and the air near the surface. The resulting fluxes were not significantly dependent on the choice of the parameters, weather measured or assumed. The coefficient of determination between the two sets of computed fluxes were 1 for both sensible and latent heats. The RMSE ranged between 0.89 and 9.22 with the highest RMSE value on day of year (DOY) with the lowest soil moisture.

MIRAMARE — TRIESTE

December 2010

                                                                                                                         1  mojisolaadeniyi@yahoo.com  2  biodunotunla@yahoo.com  

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1 Introduction

1.1 Background and Motivation

Air- earth interaction is a continuous process whereby energy and masses are exchanged continuously. Quantification of these energy and masses has been an issue of interest to various groups of researchers, and a number of measurement techniques and estimation models have been developed. Lysimeter is used to measure evapotranspiration leading to the determination of latent heat flux, eddy covariance system can also measure water vapour fluxes, carbondioxide fluxes, three dimensional wind speed from which sensible and latent heat can be determined. Surface energy fluxes are needed as inputs in climate, hydrological and agricultural models, all of which need accurate input data. Such ground data are still scarce in this part of the tropics since direct measurement of turbulent fluxes is not common here. This is due to the expenses and the technicalities involved. In stations where eddy covariance system is available, they are not used all the time but only for limited periods in order to preserve the life span of the equipment. They are used just to compliment profile measurements of meteorological variables. The surface energy fluxes are mostly estimated using various methods. The available methods have been used in various areas, Gardelin and Lindstrom (1996) used the Priestly Taylor method to estimate evaporation. Mosner and Aulenbach (2003) compared five methods (Priestly Taylor, Penman, Georgia Automated Environmental Monitoring network, Papadakis equation and DeBruin-Keijam equation) of evaporation estimation with the energy budget method in order to validate the methods. Alberton et al., 1995 used the flux variance method to estimate sensible heat flux from arid regions. Wu and Wang (2005) used the resistance based evaporation coefficient method to estimate evaporation from soil surfaces. Su (2002) used the surface energy balance system to estimate sensible and latent heat fluxes. Mafouf and Noilhan (1991) compared bulk aerodynamic formulation of five different forms to estimate evaporation from bare soil. Moram et al., 1984 computed evaporation rates on uniform surfaces using Penman Monteith equation. Konukc u (2007) computed bare soil evaporation using the Penman Monteith method and Kondo et al., 1991 constructed a soil model for the estimation of surface energy fluxes from bare soil surfaces.

At the Nigerian Micrometeorological Experiment (Nimex_1) site the Penman Monteith method needs to be validated with observed data. This investigation was designed to carry out the validation using eddy covariance measured data.

2 Method

2.1 Experiment

A group of scientists from some higher Institutions in Nigeria came together under the umbrella of Nimex. We carried out micrometeorological experiment at Obafemi Awolowo University, Ile- Ife (7033′N, 4033′E), Nigeria between 19 February and 9 March 2004. The period of investigation fell into the transition period from wet to dry season, when rain was just starting. There are two seasons viz in Nigeria which are dry (November to March) and wet (April to October). The Eddy covariance system comprising of three dimensional Ultrasonic anemometer USA-1 manufactured by METEK with the accuracy of 10 Hz and a Krypton Hygrometer made by Campbell Scientific, also with the accuracy of 10 Hz, were used to measure turbulent fluxes. Data acquisition was carried out by Datalogger CR10X. A 15 m mast was used to hang sensors for profile measurements of wind speed, air temperature (wet and dry bulb). The wind direction was measured at 14.8 m, air pressure, soil

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surface temperature, soil temperature (at three depths), soil heat flux at three depths, global radiation, net radiation (with all its components), and rainfall amount were all measured. Details of the experiments and the sensors used can be found in Jegede et al., 2004 a and b and Mauder et al., 2007.

The Bowen ratio energy balance (BREB) method and modified BREB were the commonly used methods in this area for the estimation of sensible and latent heat flux when direct measurements were not done. The performance of Bowen ratio has been found satisfactory but other available methods should be validated, possibly there can be a better method of estimation. This led to this investigation to ascertain the applicability of the Penman Monteith method in the estimation of sensible and latent heat fluxes in this area. This method has been extensively applied all over the globe especially for estimating evapotranspiration. In fact it is the recommended method for estimating evapotranspiration (Allen et al., 1998; Naijafi, 2007).

Day of year (DOY)s 61, 63, 66 and 67 were selected for this investigation based on their soil moisture content. The bushes on the experimental sites were cleared just before the commencement of the experiment.

2.2 Theory and Calculation

2.2.1 Penman Monteith Parameterization

The Penman Monteith method is an extension of the Priestly Taylor method where the evaporative cooling effect is incorporated into the Priestly Taylor parameterization for sensible and latent heat fluxes. A correction term, Fw was added to and subtracted from latent heat and sensible heat fluxes, respectively (Penman 1948, Monteith, 1965; DeBruin and Hostlag, 1982).

The resulting Penman Monteith parameterization is given by:

γγ

+

−−=

ccG

WGNH SX

FQQQ

)( (1)

γ++−

=ccG

WGNccGE SX

FQQSXQ

)( (2)

where NQ = net radiation

HQ = sensible heat flux

EQ = latent heat flux and

GQ = ground heat flux.

Scc = the rate of change of specific humidity

and γ = 0.667KhPa-1 is the psychrometric constant for p = 1000 hPa and T = 200C.

Fw is used to represent a specific humidity flux which can be approximated by a bulk transfer law of the form:

satSGEw qXXMCF ⋅−= )( (3)

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Where CE is the bulk transfer coefficient for moisture

M = the mean wind speed

GX = the relative humidity of the surface of the earth or plant

SX = the relative humidity of the air near the surface

2.3 Comparison of Penman Monteith estimated fluxes with eddy covariance measured fluxes

The estimated and measured fluxes were compared using coefficient of determination (R2) and root mean squared error (RMSE) statistics between them.

3 Results and Discussion

3.1 Result of DOY 66

The Penman Monteith method gave a good representation of both sensible and latent heat fluxes although the latent heat flux was slightly underestimated. The sensible heat flux was perfectly estimated during the day but slightly overestimated in the night Fig. 1. The coefficient of determination between measured and estimated sensible heat flux was 0.97 while that of latent heat flux was 0.89 but when the trend line was through the origin the values reduced to 0.82 and 0.81, respectively. The root mean squared error between the measured and estimated sensible heat flux was 16.48 Wm-2 while that between measured and estimated latent heat flux was 46.69 Wm-2. This method gave a better representation of sensible heat flux than latent heat flux. These errors were within an acceptable limit for diurnal variation. The average soil moisture for DOY 66 was 0.089.

 

(a)  

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(b)  

 

(c)

Figure 1 (a) Diurnal variation of estimated and measured sensible and latent heat flux for DOY 66 (b) Scatter plot of estimated and measured sensible heat flux for DOY 66 (c) Scatter plot of estimated and measured latent heat flux for DOY 66  

3.2 Result of DOY 67

On DOY 67 both sensible and latent heat fluxes were well estimated. The coefficient of determination of 0.92 and 0.86 were obtained between estimated and measured sensible and latent heat fluxes, respectively. The values reduced to 0.86 and 0.82 respectively when the trend lines were shifted to the origin. The root mean squared errors were 19.42 and 39.69 respectively for sensible and latent heat fluxes, Fig. 2. These errors were fine for diurnal variation. The average soil moisture for DOY 67 was 0.083.

 

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(a)  

 

(b)  

 

(c  )  

Figure 2 (a) Diurnal variation of estimated and measured sensible and latent heat flux for DOY 67 (b) Scatter plot of estimated and measured sensible heat flux for DOY 67 (c ) Scatter plot of estimated and measured latent heat flux for DOY 67

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3.3 Result for DOY 63

This model gave a perfect estimation of both sensible and latent heat fluxes on DOY 63. The coefficient of determination between estimated and measured fluxes was 0.92 for sensible heat and 0.92 for latent heat. The values reduced to 0.89 and 0.90 respectively when the trend lines were set at the origin Fig. 3. The mean soil moisture for the day was 0.11. The root mean squared errors between estimated and measured fluxes were 17.53 Wm-2 and 39.16 Wm-2 for sensible and latent heats, respectively.

 

(a)  

 

(b)  

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(c)  

Figure 3 (a) Diurnal variation of estimated and measured sensible and latent heat flux for DOY 63 (b) Scatter plot of estimated and measured sensible heat flux for DOY 63 (c ) Scatter plot of estimated and measured latent heat flux for DOY 63

The Penman Monteith method performed well in estimating sensible and latent heat fluxes on DOY 61 like the other DOYs, Fig. 4. However, the latent heat flux for this day has higher error than the other DOYs, RMSE =22.17 Wm-2 for sensible heat flux and 72.96 for latent heat flux. The coefficients of determination between estimated and measured fluxes were 0.91 and 0.85 for sensible and latent heats, respectively. When the trend lines were shifted to the origin the coefficients of determination reduced to 0.84 and 0.78 for sensible and latent heat fluxes, respectively.

 

(a)  

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(b)  

 

(c)  

Figure 4 (a) Diurnal variation of estimated and measured sensible and latent heat flux for DOY 61 (b) Scatter plot of estimated and measured sensible heat flux for DOY 61 (c ) Scatter plot of estimated and measured latent heat flux for DOY 61

The Penman Monteith method gave estimated sensible and latent heat fluxes that are comparable to results from other models. Moram et al., 1984 came out with root mean squared error of 29 Wm-2 (not diurnal) between measured and estimated latent heat flux. Our own results for diurnal variation were 38.72, 39.87, 49.15 and 76.08 Wm-2. Su (2002) obtained RMSE of 21.22 Wm-2 for sensible heat flux, our result showed RMSE range for sensible heat flux from 17.63 to 22.11 Wm-2. He obtained RMSE of 29.22 Wm-2 for latent heat flux (not diurnal). Our diurnal RMSE values were a little higher than this. He obtained R2 value of 0.81 and 0.43 for sensible and latent heat fluxes, respectively. Our R2 value ranged from 0.83-0.9 and 0.78-0.9 for sensible and latent heat fluxes, respectively. Wu and Wang (2005) obtained R2 of 0.88 for evaporation from soil surfaces. Our result compares well with this. Albertson et al., 1995 also got R2 value of 0.85 between observed and estimated sensible heat flux, which is comparable to our result.

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3.4 The Ruggedness of the Penman Monteith model

The specific humidity term in equations (1), (2) and (3) require values of XS, XG andM .

M , XS, XG and temperature can all be measured. It is also possible to estimate XG and XS from global relative humidity or from the knowledge of average soil moisture content.

We found sensible and latent heat fluxes using the measured parameters and we also found the fluxes using approximated values for the parameters XS, XG . Relative humidity of the earth (loamy soil) varies from 0 to 1 when soil moisture is less than 0.1. The soil on Nimex 1 field is loamy sand. Relative humidity is constant with soil moisture when the soil moisture is greater than 0.15, between 0.1 and 0.15, there is a sharp variation (Kondo et al., 1990). We took XG to be 0.9 since the period of experiment was a transition period from dry to wet season, there were few and scattered rains and soil moisture was between 8 and 14 %. XS was taken to be 0.5 since there is a general reduction in the value of relative humidity with distance from the earth surface (Peixoto and Oort, 1996). Comparing the two set of estimated fluxes there were no significant difference. We found root mean squared errors of 2.61, 0.88, 4.74 and 9.22 for both sensible and latent heat fluxes on DOY 61, 63, 66 and 67, respectively. The coefficients of determination for both fluxes were very high, they were found to be 1 for sensible and latent heat fluxes respectively on all the DOYs, Fig. 5.

Since both measured XG and XS gave almost the same surface fluxes, it may not be necessary to measure them, this reduces cost and the same quality of result is assured. All the required meteorological parameters can be collected from the data bank of Meteorological Agencies with which larger areas can be effectively covered.

 

 

(a)  

 

 

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(b)  

 

(c)  

 

(d)  

 

 

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(e)  

 

(f)  

 

(g)  

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(h)  

 

(i)  

 

(j)  

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(k)  

 

(l)  

Figure 5: (a) Diurnal variation of Penman Monteith estimated sensible and latent heat fluxes from measured and estimated parameters for DOY 61 (b) Scatter plot of sensible heat flux computed from estimated and measured parameters for DOY 61 (c ) Scatter plot of latent heat flux computed from estimated and measured parameters for DOY 61 (d) Diurnal variation of Penman Monteith estimated sensible and latent heat fluxes from measured and estimated parameters for DOY 63 (e) Scatter plot of sensible heat flux computed from estimated and measured parameters for DOY 63 (f) Scatter plot of latent heat flux computed from estimated and measured parameters for DOY 63 (g) Diurnal variation of Penman Monteith estimated sensible and latent heat fluxes from measured and estimated parameters for DOY 66 (h) Scatter plot of sensible heat flux computed from estimated and measured parameters for DOY 66 (i) Scatter plot of latent heat flux computed from estimated and measured parameters for DOY 66 (j) Diurnal variation of Penman Monteith estimated sensible and latent heat fluxes from measured and estimated parameters for DOY 67 (k) Scatter plot of sensible heat flux computed from estimated and measured parameters for DOY 67 (l) Scatter plot of latent heat flux computed from estimated and measured parameters for DOY 67  

4 Conclusion

The Penman Monteith model gave comparable estimated sensible and latent heat fluxes to the measured eddy covariance fluxes. However, it gave a better estimation of sensible heat flux than

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latent heat flux. The performance of the model is comparable to the performance of other surface energy estimation models.

The model was found roughed in the choice of parameters for the advective correction term such that assumption of the ground and near earth relative humidity was acceptable based on the prevailing weather condition. The fluxes computed with measured parameters and those with assumed parameters were found comparable. This model constitutes an easy and reliable method in the estimation of surface energy fluxes on the Nimex 1 site.

Acknowledgments

This research was supported by International Programmes in the Physical Sciences (IPPS) Sweden, African Regional Centre for Space Sciences and Technology Education, Ile- Ife, Nigeria National Space Research and Development Agency, Abuja, Nigeria. The work was prepared at the Abdus Salam International Centre for Theoretical Physics, Trieste Italy. The authors appreciate the efforts of other members of the Nimex group for making this research a reality.

References

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