Estimating Spatial Distribution of Air Temperature from Meteorological Stations Using Atmospheric Model

Planning agricultural procedures needs to take into account meteorological conditions. However, because of high associated costs, the density of meteorological stations is often not enough to cover all the cultivated or potentially cultivated areas. In this article we present a methodology to estimate seasonal maximum and minimum mean temperature in cultivated area using data registered in a sole or a few meteorological stations. The procedure is based on mesoscale modeling, which allows meteorological variables to be spatially distributed considering synoptic data and local characteristics. Simulated daily cycle of temperature was compared with data registered at six meteorological stations located in the cultivated floor of the semiarid Limari Valley (Chile, 31°S). Although in some cases the simulated temperature differs in about 2°C with the observed one, a good fit between model results and experimental data was observed. Using the simulated seasonal minimum and maximum mean temperature fields, maps of temperature differences with respect to a reference station were drawn. In order to observe the influence of the orography on the lapse rate around a station, the methodology was applied for two reference stations located in places with different orographic characteristics. Results for winter and summer seasons are shown. These generated maps can be used by farmers and agricultural planners to obtain information of seasonal minimum and maximum mean temperature from a station in any site of the cultivated area. This technique is a good alternative to obtain meteorological information at low costs, contributing to territorial planning for climate resilient agriculture sustainability.


Introduction
Agricultural productivity is severely affected by meteorological parameters such as rainfall, wind speed, solar radiation and air temperature (Hatfield et al., 2011).The break of dormancy, growth rate, fruit quality, and yield production are influenced by changes in environmental conditions (Griffiths, 1994;Steel & Greer, 2008;Walkovszky, 1998;Salazar-Parra, Aguirreolea, Sánchez-Díaz, Irigoyen, & Morales, 2010).Because of the close relationship between meteorology and yield production, knowing the meteorological characteristics of a site could help the selection of crops and cultivars best adapted to the area.Therefore farmers often install meteorological stations within their cultivated area.However, it is an expensive undertaking, and currently many cultivable places do not possess a sufficient number of meteorological stations.For this reason, farmers use the nearby station to get meteorological information.However, the validity of this procedure depends on spatial distribution of the meteorological variable in the area (Gomez et al., 2008;Lookingbill & Urban, 2003), factors for which confidence data are generally not known.
Among the environmental factors, the temperature is one of the most relevant variables in yield production.Maximum and minimum temperatures influence bud formation, shoot growth, time of flowering, fruit formation, ripening, harvest, fruit size and fruit quality (Thuzar, Puteh, Abdullah, Mohd-Lassim, & Jusoff, 2010;Ferris, Ellis, Wheeler, & Hadley, 1998;Wheeler, Craufurd, Ellis, Porter, & Vara-Prasad, 2000).temperature (Kalthoff et al., 2006).Many authors have developed different techniques to spatially distribute temperature records.For example, Gomez et al. (2008) used mathematical interpolation of data registered in meteorological stations improved with climate data, and Lookingbill and Urban (2003) evaluated temperature distribution in a mountain environment from a network of portable temperature micro-loggers and using environmental information such as radiation and slope.
Unlike the methods mentioned above, atmospheric modeling allows the evaluation of temperature taking into account both orographic and synoptic conditions, as well as the physical processes relevant for the temperature behavior (Holton, 1992).Besides, it is possible to calculate values of temperature not only at a single point, but in an extended area.Therefore atmospheric modeling can be a useful tool to estimate temperature at sites without meteorological information.
In this article we report a methodology based on atmospheric modeling, which allows the estimation of temperature over an area from data registered at a meteorological station.This procedure was applied to the cultivated area of the Limari Valley, located in the semi-arid Norte Chico of Chile.We used the KAMM Model (Karlsruhe Atmospheric Mesoscale Model) to evaluate seasonal mean temperature fields over a period of 16 years.This period is large enough to consider interannual variability.To ensure the validity of the model, simulation results were compared with data of meteorological stations located on the cultivated floor of the valley.
We applied the methodology to spatially distribute mean seasonal maximum and minimum mean temperature.Although the study can be performed for all seasons, in this article the results only for the extreme winter and summer were presented.The procedure shown here allows the generation of maps that can be used by farmers to estimate the mean temperature with respect to a reference station (RS).These maps could be used to incorporate climatic factors in crops and territorial planning.

Study Site
The Limari basin (31ºS-31.5°S) is located in the semi arid Norte Chico of Chile, south of the hyperarid Atacama Desert and about 350 km north of Santiago de Chile.It extends from the Pacific Ocean eastwards to the Andes Cordillera with elevations until 4500 m.It has an important agricultural activity with a cultivated surface of about 46000 ha.Grapes for table and wine production are the most important cultivars in the valley (Ibacache & Sierra, 2009).
The mean annual precipitation of the Norte Chico varies from approximately 100 mm at the coast to 300 mm at the top of the Andes.It has an important orographic influence (Favier, Falvey, Rabatel, Pradeiro, & Lopez, 2009) with a Mediterranean rainfall regime and precipitation occurs predominantly in winter months, during the passage of frontal systems from the southern Pacific (Falvey & Garreaud, 2007).The interannual variability of precipitation is strongly influenced by the El Niño Southern Oscillation, with higher than average amounts during the warm phase (Rutllant & Fuenzalida, 1991).As a consequence of these characteristics, it was necessary to build artificial lakes to provide water for irrigation, making agricultural productivity less dependent of precipitation.
At the coastal zones the sea breeze can carry humid and cold air from the ocean to the inland zones (Luebert & Pliscoff, 2006;Kalthoff et al., 2006), which generates a longitudinal climatic gradient, along the East-West oriented valleys such as Limari.
The study site is represented in Figure 1c.It includes the entire cultivated area of the Limari valley, and it covers an area of 70 x 50 km 2 between 71.5ºW and 70.7ºW of longitude and 31.0ºS and 30.9ºS of latitude.Figure 2 shows the topography (a) and land use classification (b) of the study site.

Mesoscale Modeling
The numerical simulations were performed with the three-dimensional non-hydrostatic Karlsruhe Atmospheric Mesoscale Model (KAMM; Adrian & Fiedler, 1991).The model consists of two components, the atmospheric and the soil vegetation module (Schaedler, Kalthoff, & Fiedler, 1990).It solves the momentum, heat, and humidity equations, transformed onto a coordinate system which follows the terrain.It needs as input data information from the large-scale synoptic weather situation (profiles of temperature, humidity and wind) as well as topography, soil types and land use.More information about the model can be found in Bischoff-Gauß, Kalthoff, and Fiebig-Wittmaack (2006); Montecinos, Boersch-Supan, Favier, Astudillo, and Tracol (2008).
We evaluated the mean meteorological conditions for a period of 16 years, from 1990 to 2006.The methodology was based on cluster analysis (Anderberg, 1973;Ward, 1963), which is a method to identify groups or clusters with common patterns.The variables selected to define similarity were i) zonal wind, ii) meridional wind, both at 500 hPa pressure level, and iii) vertical potential temperature gradient (Holton, 1992) between 850 hPa and 500 hPa.
The mean meteorological conditions were calculated as follow: for each cluster a simulation with the KAMM model was performed.The initial profiles of temperature, humidity and wind needed to initialize the model, were calculated by taking an average over all members of the cluster.The profiles were taken from the National Center for Environmental Prediction/NCAR Reanalysis (Kalnay et al., 1996).
The mean meteorological characteristics were calculated by averaging the cluster simulations, taking into account the specific weight of each one.

Simulation Region and Model Setup
The simulation region is shown in Figure 1b.It is located within the semi-arid zone of the Norte Chico of Chile, south of La Serena city.It covers an area of 256 x 303 km 2 between 72.0ºW and 70.2ºW of longitude and 31.8ºS and 30.2ºS of latitude.The region includes the transversal Limari and Choapa valleys.The terrain is complex, with heights that vary from the sea level at the Pacific coast to 5500 m at the Andes Cordillera.
The upper limit of the model was set at 10 km altitude.The simulation region was divided horizontally into 1×1 km 2 cells and vertically into 40 layers.The land use classification was taken from CONAF and CONAMA (1999).
The land use classes were adapted to the KAMM land use classification and some new categories were aggregated, so that 14 classes remain in the model.
The environmental input data were taken from the following sources: initial vertical profiles from National Center for Environmental Prediction/NCAR Reanalysis (Kalnay et al., 1996); earth surface temperature was set 1°C colder than the lower air temperature, inferred from experimental data registered at the meteorological station San Carlos (30.06°S,70.82°W).The temperature of the Pacific Ocean was taken from satellite data (reference in Reynolds, Rayner, Smith, Stokes, & Wang, 2002).

Spatial Estimation of Air Temperature Based on a Reference Station (RS)
We used atmospheric model for evaluating the mean fields of minimum and maximum temperature, in winter (June, July and August) and summer (December, January and February), over the study site.In all cases, the mean temperature field ( ) was evaluated at 2 m above ground level, according to the standard height of the temperature sensor in agrometeorological stations.
In order to estimate the temperature from a RS, we evaluated the field of temperature difference  and o T , were simulated results obtained with the KAMM model.The procedure described above was performed for four cases: minimum and maximum temperature, for winter and summer.
The field of temperature differences was evaluated separately for two RS on the cultivated floor of the valley: La Chimba and San Antonio, two locations that are indicated in Figure 2a by 1 and 2, respectively, and by red points in Figure 2b.These stations are located on different orographic conditions: La Chimba (30.59°S, 71.14°W, 270 m above mean sea level), on the flat valley floor surrounded by cultivated areas, and San Antonio (30.74°S, 70.93°W, 485 m above mean sea level), on a hill in the proximity of the Andes Cordillera, and about 1 km east of a water reservoir (Figure 2).These stations were chosen to test the method on two different and contrasting conditions.

Model Validation
In order to verify whether the model reproduces the near surface climatic near surface characteristics of the valley system, model results were compared with the observed ones in six meteorological stations located in the study site.Figure 3 displays the mean diurnal cycle of temperature simulated and observed at six meteorological stations.The graphics 3a to 3f correspond to the results in winter, and from 3g to 3l to summer.The number of the station is indicated at the top of each graphic, and its location is shown in Figure 2a.Although in winter and summer some differences between model results and observations are observed, these differences are at the most 2°C (Figure 3).Moreover, the Root Mean Square Error between the simulated and observed temperatures in winter and summer varies between 0.2°C and 0.5°C.So it can be concluded that the model in general satisfactorily describes the temperature behavior in the cultivated area of the Limari Valley, and can potentially be used to obtain secondary information applicable to the agriculture.The spatia summer (F high moun

Spatial
We evalua respect to Chimba an continuous site into z position of green zone the absolu 3°C, becau In the case of La Chimba station (Figure 5), in all events a smooth variation of temperature around the station was observed.In winter and summer, the minimum temperature varies less than the maximum one.In the case of maximum temperature, the points outside the range of 3°C observed in winter (Figure 5b) and summer (Figure 5d), fall outside the cultivated zone.
We note that the variation of temperature around San Antonio is higher than in La Chimba, which could be attributed to the orographic characteristics of the location of San Antonio station and differences in soil use, all of which alters surface energy balance, thereby inducing differential heating rates of the ground (Kalthoff et al., 2006).

Discussion
In this article a methodology based on atmospheric modeling to estimate the mean temperature in cultivated areas from data registered in one meteorological station was proposed.We used the KAMM model to evaluate mean temperature fields, in winter and summer, and the results were compared with data of six meteorological stations.
A good fit between data and model results was found.
Model results were used to draw maps of minimum and maximum temperature differences between the study site and the temperature at a RS.Both, the temperature at the study site and the one at the RS, were simulated results.This procedure was performed for winter and summer, using two RS, located at places with different orographic conditions.
The resulting maps can be used by farmers to estimate the mean minimum and maximum temperature in any place of the cultivated area.For example, if a farmer wants to know maximum temperature in summer based on data records in La Chimba station, he/she should use the map shown in Figure 5d.If the site is the one indicated by the arrowhead (Figure 5d) the farmer can estimate the maximum temperature adding 3ºC to the maximum temperature recorded in La Chimba.We remark that when the temperature is operating at its extremes in winter or summer months during crop season in the agricultural field, these maps may be used cautiously.
This technique can be applied for any variable, such as mean temperature, evapotranspiration, wind velocity and humidity.The methodology shown in this article can be reproduced in any site, using the KAMM model or other mesoscale model, such as Weather Research and Forecasting WRF model (http://wrf-model.org).
It is important to mention that the spatial resolution used in mesoscale modeling limits the validity of the results.If the study area has a very complex topography, it could be necessary to increase the spatial resolution of the model simulations.
Using atmospheric mesoscale models would enable the reduction of costs associated with maintenance and/or installation of meteorological stations, even in areas with complex topography.Further, it allows to know temperature using a RS, not only in the cultivated area but beyond, enables the assessment of new cultivable ones.

Figure 1 Figure
Figure 1 over the entire study site.

Figure 3 .
Figure 3. Simulated and observed diurnal cycles of temperature in winter (a), b), c), d), e) and f)) and summer (g), h), i), j), k), l)) at six meteorological stations in the Limari Valley.At the top of each graphic the number marking the station is indicated, which location is shown in Figure 2 Figure maximum