A novel approach for estimating the pan coefficient of irrigation water reservoirs: Application to South Eastern Spain

https://doi.org/10.1016/j.agwat.2007.04.011Get rights and content

Abstract

The evaporation rate (E) and pan coefficient (Kp) of agricultural water reservoirs for irrigation (AWRIs) were determined using a novel approach based on a reservoir energy balance model and measurements of pan evaporation. The model, previously developed and validated for an insulated Class-A pan, was upscaled to the case of AWRIs by introducing a new formulation of the wind function combining the Brutsaert and Harbeck formulae. The model was run for different combinations of area (S) and depth (D) at several locations of the Segura River Basin (South Eastern Spain) where routine pan evaporation measurements (Ep) were available. The monthly and annual Kp values were derived from the simulation runs as the ratio of the simulated AWRI evaporation to the measured pan evaporation, E/Ep. Results at a monthly scale indicated that D was the main factor affecting the evolution and the value of the surface temperature and evaporation rate, while S, for a given value of D, had only a small influence. Monthly Kp varied significantly through the year, the variation range being larger for deep AWRIs (0.5 < Kp < 1.5) than for shallow ones (0.8 < Kp < 1.2). At a yearly scale, Kp was found nearly constant for a given AWRI, with small inter-annual variations. Annual Kp varied in the range 0.76 (S = 50,000 m2) to 0.86 (S = 500 m2), depending primarily on S, and to a lesser extent, on the vapour pressure deficit measured at the location. Empirical formulae allowing to predict annual Kp as a function of S and vapour pressure deficit were proposed. It was concluded that the proposed modelling approach can be applied to accurately estimate values of Kp in AWRIs at regional scale, taking into account the influence of reservoir dimensions and local climate conditions. Its application under South Eastern Spain conditions supplied the monthly and annual values of Kp to be used under similar Mediterranean semi-arid climates.

Introduction

Estimation of evaporative losses is of paramount importance for the monitoring, survey and management of water resources, at a farm scale as well as at a regional or catchment's scale (Morton, 1990, Bruton et al., 2000, Stanhill, 2002). In the case of agricultural water reservoirs for irrigation (AWRIs), evaporation losses can represent a significant fraction of the total water stored during the irrigation season (Hudson, 1987, Mugabe et al., 2003) and could be a serious constraint for irrigation water-availability under arid and semi-arid conditions. Valuation of techniques for increasing AWRI storage efficiency, such as shading structures (Martínez Alvarez et al., 2006), requires an accurate estimation of the amount of evaporated water. Therefore, it is of primary interest to estimate AWRIs evaporation rate, either from measurements or from formulae and models (Lenters et al., 2005).

The simplest way to estimate AWRI evaporation would be to use pan evaporation data, Ep. This method is commonly used to derive the evaporation over water surfaces, E, for hydrological applications (Linsley et al., 1992), or the reference crop evapotranspiration, ET, for agricultural and irrigation purposes (Doorenbos and Pruitt, 1977, Allen et al., 1998, López-Urrea et al., 2006). For both types of application, an empirical pan coefficient, Kp, defined as the ratio of E (or ET) to Ep is used to supply an estimate of either E or ET.

Regarding lake evaporation, annual Kp was found to be about 0.70 (Linacre, 2004), with a wide variation range from 0.6 to 0.82 (Kohler et al., 1955). The excess of evaporation from the pan with respect to lakes or reservoirs is due to the heat transfer processes occurring at the pan walls (side and bottom), which induce a net gain of energy to the water body and therefore enhance the evaporation rate. The variation of the annual Kp was related to the local climate conditions, increasing with relative humidity (Eagleman, 1967) and decreasing with the evaporation rate (Stanhill, 1976), suggesting that the relative contribution of the energy gain through the walls to evaporation losses is probably higher in warm and dry climates than in humid and cold ones. Other authors related the variation of the annual Kp to the dimension of the water body. Guobin et al. (2004) investigated the evaporation from pans with different areas (0.1–100 m2) and observed significant variations with respect to the Class-A pan (≈1 m2). Webster and Sherman (1995) justified the decrease of Kp with the water body area as a result of the modification of the temperature and specific humidity of the air that flows over the water surface with distance downwind. At a seasonal scale, substantial variations of Kp due to the thermal inertia of the water body were reported (Allen and Crow, 1971). The above considerations clearly indicate that the main drawback of the pan approach is the uncertainty about the value of the pan coefficient to be applied and point out the interest of assessing the influence of reservoir dimensions and local climate conditions on Kp. Current alternatives to the Kp approach are:

  • (i) To use semi-empirical relationships relating E to the variables involved in the surface energy balance and the mass transfer process, such as global solar radiation, Rs, wind speed, U, air temperature, Ta, and air vapour pressure deficit, VPD (Brutsaert, 1982, Singh, 1989, Morton, 1994, Winter et al., 1995, Xu and Singh, 2000, Xu and Singh, 2001). The Penman formula (Penman, 1948), based on the combination of the surface energy balance and an aerodynamic formula (wind function), is widely used for estimating the evaporation from a free water surface. Another option is the mass transfer method (Sartori, 2000, Singh and Xu, 1997), which requires the knowledge of the water surface temperature, Ts.

  • (ii) The estimation of Ts by solving numerically the energy balance at the water body surface, using as model inputs the climatic data routinely available at meteorological stations. This approach was applied for studying the daily and annual evolution of Ts in Class-A pan evaporimeters and their influence on the pan evaporation rate, Ep, considering an isothermal behaviour (Jacobs et al., 1998, Molina Martínez et al., 2006).

The abovementioned considerations underpin the importance of investigating more thoroughly the relationships between Ep and the estimates of E derived from numerical models which account for the specific dimensions and location of the AWRI. Therefore, the main aim of this study was to propose an original modelling approach with universal applicability for assessing the values of Kp in AWRIs at regional scale. The modelling approach was based on the simulation of the daily energy balance of the water body, using a mechanistic model which supplies daily values of Ts and E. Its application to several locations of a semi-arid region (Murcia, Segura River Basin, South Eastern Spain) was carried out, supplying the values of Kp for different reservoir dimensions, at both monthly and yearly scales.

Section snippets

Pan evaporation and climatic data

Six automated meteorological stations of the Servicio de Información Agraria de Murcia (SIAM) were selected for the daily data needed as input of the model. Two of them were located in the coastal plain (San Cayetano and Mazarrón), two were in the Guadalentin Valley, about 50 km inland (Murcia and Alhama de Murcia), and the last two (Abarán and Jumilla) were about 100 km inland (Fig. 1). All the locations are representative of irrigated areas (mainly horticultural crops, orchards and vineyards)

General trend of observed pan evaporation and climate

The Segura River Basin (Fig. 1) is characterized by a Mediterranean semi-arid climate, with warm and dry summers and mild winter conditions. Annual rainfall is typically around 350 mm, presenting high seasonal and inter-annual variability. Most of the rains occur during the fall and winter seasons. Globally, the six locations showed the same yearly trend in Ep. The differences between stations were relatively small, as it can be seen in Fig. 4 where the evolution of the average monthly values of

Concluding remarks

This work demonstrated that simple modelling tools that allow accounting for the dimensions of water bodies and the local weather conditions in predicting evaporation losses could be of help and interest to water engineers and hydrologists. The adopted methodology proved to be robust and realistic, as the outputs of the model (E and Kp) appeared to be coherent and in agreement with previous works carried out on water bodies or shallow lakes of different areas and depths under similar climatic

Acknowledgement

The authors acknowledge the Fundación Séneca (Murcia, Spain) for the financial support of this study through the grant 02978/PI/05.

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