Predicting Downward Longwave Radiation for Various Land Use in All-Sky Condition: Northeast Florida

Accurateestimateofthesurfacelongwaveradiationisimportantforthesurfaceradiationbudget,whichinturncontrolsevaporationandsensibleheatfluxes.Regionallandusechangescanimpactlocalweatherconditions;forexample,heterogeneouslandusepatternsandtemporalchangesinatmosphericcirculationpatternswouldaffectairtemperatureandwatervaporpressure,whicharemorecommonlyusedasinputsinexistingmodelsforestimatingdownwardlongwaveradiation(LW d ). In this study, first, we analyzed the cloud cover and land use covers impacts on LW d . Next, LW d on all-sky conditions were developed by using the existing land use-adapted model and cloud cover data from the region of Saint Johns River Water Management District (SJRWMD), FL. The results show that factors, such as, seasonal effects, cloud cover, and land use, are of importance in the estimation of LW d and they cannot be ignored when developing a model for LW d prediction. The all-sky land use-adapted model with all factors taken into account performs better than other existing models statistically. The results of the statistical analyses indicated that the BIAS, RMSE, MAE, and PMRE are − 0.18Wm −2 , 10.81Wm −2 , 8.00 Wm −2 , and 2.30%; − 2.61 Wm −2 , 14.45 Wm −2 , 10.64 Wm −2 , and rangeland, and


Introduction
Accurate estimate of downward longwave radiation (LW d ) is necessary for calculating the net radiation, which in turn modulates the magnitude of the surface energy budgets, including latent heat [1].This knowledge is also required for (a) forecasting of temperature variation, frost occurrence, and cloudiness, (b) estimation of climate variability and global warming, and (c) design of radiant cooling systems [1,2].
The downward longwave radiation is a thermal infrared energy (in the wavelength of 4.0-100 m), mainly controlled by water vapor and aerosols such as cloud water droplets, CO 2 , and O 3 molecules [3].The longwave radiation is more difficult and expensive to measure than shortwave radiation because it is not a conventional measurement and thus its measurement is rarely included in meteorological stations [4].Moreover, due to poor vertical resolution of water vapor data and difficulties associated with the atmospheric emissivity and temperature, many reasonably successful techniques have been developed in recent decades that estimate LW d based on the screen-level humidity and air temperature measurements.Angstrom [5] first observed an empirical relationship between downward longwave clear-sky irradiance and vapor pressure.Following his pioneering work, several parameterizations have been developed for LW d using synoptic observations [6][7][8][9][10][11][12][13][14][15].
The major drawback of previous studies is that their methods did not perform well in other locations, since they utilized local empirical coefficients.This is mainly caused by the significant variation of the coefficients in those models, due to the variability of air temperature and water vapor pressure, which in turn resulted from the spatial change in land use pattern and temporal change in atmospheric circulation.At land scale, human activities 2 Advances in Meteorology affect regional climate by changing the land use characteristics that impact the distributions of ecosystem, energy (latent and sensible heat), and mass fluxes (e.g., water vapor, trace gases, and particulates).These contrasting land use patterns induce convection and circulation that affect the cloud formation and precipitation.For example, when large areas of forest are cleared, reduced transpiration results in less cloud formation, less rainfall, and increased drying of the earth surface [16].Previous studies on measurement of some radiation components (incoming shortwave radiation or net energy balance) focused on specific land use type, such as grass, short vegetation, bare soil, forest, and few crops, but disregarded urban areas and water-covered areas [17][18][19].
Therefore, a long-term monitoring and modeling of radiation components especially longwave radiation on various land use types including urban and wetland areas rather than agricultural and rangeland areas only are essential and critical.Rizou and Nnadi [15] developed a land use-adapted model which superpositioned nonlinear temperature effects and water vapor in one equation to account for the net impact on clear sky emissivity.Their model was robust and adaptable for different land use areas.The statistical parameters, including normalized mean bias errors (MBE) and root mean square errors (RMSE), are smaller than those of other existing models, which showed the model's good performance relative to others.In their study, three-month data in spring 2004 at current study area were analyzed but the seasonal variation and cloud effect were not considered on the various land use effects.
Culf and Gash [9] in considering a sinusoidal variation between wet and dry season showed that the leading coefficients of LW d regression model were different.This is similar to other meteorological variables, such as temperature, solar radiation, and water vapor pressure.In the dry season, the lapse rate of water vapor is lower than a standard atmosphere.On the other hand, the wet season is more humid and has a higher water vapor lapse rate.Other studies suggested that seasonal analysis and adjustment of LW d model are necessary and critical in long-term analysis [1,4,12].
Rizou and Nnadi [15] indicated that the clouds would result in more noise in diurnal pattern of radiation, while Crawford and Duchon [1] argued that the utility of most techniques applicable to clear sky has great limitations.Previous studies also suggested that cloud cover plays an important role in preventing radiation deficit.These studies stated that thick clouds primarily reflect solar radiation and cool the surface of the earth, while high and thin clouds mainly transmit incoming solar radiation.However, it was also suggested that thick clouds trap some of the outgoing infrared radiation emitted by the earth and radiate it back downward, thereby warming the surface of earth.Therefore, several researchers have proposed locally adjusted equations for LW d fluxes in cloudy condition, such as Jacobs [8] for Baffin Island, Canada, Maykut and Church [7] for Alaska, United States, Sugita and Brutsaert [20] for Kansas, United States, Konzelmann et al., [21] for Greenland, and Crawford and Duchon [1] for Oklahoma, United States.

Parameterization Schemes
2.1.Basic Emissivity Model.Rizou and Nnadi [15] developed a land use-adapted model based on slab emissivity by Elachi [22]: where  0 is the incoming wave intensity,  is the total extinction coefficient (including absorption and emission), and  is the slab thickness.The term  is usually called the optical thickness or depth.
In their study, the authors suggested that either temperature or humidity parameters can capture all LW d over a wide range of climatic conditions because of the compensating effects of temperature and water vapor.Therefore, the following equation, which superpositioned the two effects in one equation, was generated for the daily LW dc : where  1 ,  2 ,  3 , and  4 are site-specific constants and   is the emissivity of the atmosphere,  (= 5.67 × 10 −8 W/m 2 K 4 )  is the Stefan-Boltzman constant, and  is the air temperature.With the use of multiple nonlinear regression analysis, the values of the parameters were obtained for all sites.Because temperature and water vapor variation affect cloud cover, the present study developed a form of (2a) by considering seasonal variation and cloud effects.

Existing
All-Sky Parameterizations.The presence of clouds results in warmer air temperatures and also increases the amount of longwave radiation reaching the earth surface.Therefore, various studies considered cloud effect in estimating downward longwave radiation [1,4,12,14].Most of their approaches adjusted   for the fraction of cloud cover, , to compute the increase in radiation.Equations (a) through (d) in Table 1 were developed for estimating all-sky downward longward radiation in which the cloud cover  was based on human observations.In determining , the sky condition was divided into 10 sectors and the fraction of 10 was used to estimate the cloud fraction [12].However, in some study areas, the cloud cover data were absent due to lack of observers [1,4,12,14].In their later study, Crawford and Duchon [1] generalized the effect of clouds, as shown in (3), by introducing a cloud fraction term clf, defined as clf = 1−, in which  is the ratio of the measured solar irradiance to the clear-sky irradiance: where  is the numerical month (e.g., January = 1) and  is the vapor pressure (mbar).
A general limitation and drawback of this approach are that it can only be used during the daylight hours.In order to avoid this limitation, this study uses the cloud fraction data of automated surface observing system (ASOS) for developing the all-sky LW d model.The cloud amount is determined by a laser beam ceilometer with a vertical range of 3600 m where the beam's width is 18 m.The ASOS cloud sensor has a 0.9 microns wavelength, a nominal pulse frequency of 770 Hz, and sampling frequency of 30 s with an average interval of 30 min.Thus the daily average cloud cover is based on 30 min internal cloud cover.The cloud fraction is recorded in oktas with a maximum error of 5% [23].
Table 2 shows ASOS cloud gradation used in this study to develop cloud cover fractions.Laser beam ceilometers have an advantage over human observers.Traditionally, observers must wait for their eyes to adapt to the dark before they are able to accurately distinguish nighttime sky condition, while laser beam can adapt to night conditions.Another advantage of laser beam ceilometers is that it reports the onset of lower stratus moving over the ceilometer within 2 min and the formation/dissipation of a low ceiling within 10 min [23].
The equivalent oktas as defined by ASOS was further reduced to cloud cover fractions based on the average values (Table 2).Using the cloud cover fractions developed, the general form of all-sky LW d adjusted equation is given as where  is cloud cover fractions and ,  in general depend on cloud characteristics, and with the use of multiple nonlinear regression analysis, the values of the parameters were obtained for all sites.Lindsey Citrus is an agricultural site with short grass beneath the tree canopy, which is under regular irrigation schedule.At these sites, the longwave and shortwave radiation fluxes were measured by pyrgeometers (CG3 radiometers with spectral range 5-50 m, by Kipp and Zonen) and pyranometers (CM3 radiometers, by Kipp and Zonen), respectively.The expected accuracy of the CG3 sensor has a limit of ±10% for daily totals and ±20 W/m 2 for individual measurements as provided by the manufacturer [24].The steps of sensor calibration and the data quality assurance are listed below [15].(1) We compared the simultaneous field measurements and reference sensor data twice a month.Measurements that differ more than ±3% would be documented.(2) For consistency purpose, we also compared data from other regional sensors, including the incoming LW radiation data and incoming SW radiation data.If peaks in LW coincided with nadirs in SW radiation, it usually indicated a shadowing effect on the sensor.These data are removed from the dataset.(3) In addition, LW data are also compared with sensor temperature data and low battery voltage reports.When the sensor heater has been deactivated due to low battery reading, the LW data are compared with incoming SW data.

Data Collection
The ASOS HO-83 hygrothermometer was used for temperature measurements, which uses a resistive temperature device (root mean square errors (RMSE): 0.5 ∘ C, max error:   point temperature.The sampling frequency for both devices is one minute with averaging interval of 5 minutes.Water vapor pressure data were obtained by daily averaging of the dew point temperature from NOAA data.The water vapor pressure at the surface was calculated using (5) [25]: where  0 (hPa) is the actual water vapor pressure at the surface and   ( ∘ C) is the dew point temperature.

Seasonal Variation.
The wet season in Florida starts from end of May to middle of October while the rest is classified as dry season.The longwave radiation is higher and stable during wet season and lower with relative large variation during the dry season.Figure 2 shows the observed downward longwave radiation seasonal variation for all land uses.The LW d ranges from 230 to 440 Wm −2 in the four sites in the study area during the year 2004.The LW d ranged from 381 to 441 Wm −2 , 363 to 432 Wm −2 , 359 to 431 Wm −2 , and 349 to 436 Wm −2 , in Deland, Orange Creek, Ocklawaha Prairie, and Lindsey Citrus, respectively, during the wet season.The LW d in city of Deland (urban area), Orange Creek (rangeland), Ocklawaha Prairie (wetland), and Lindsey Citrus (agriculture), varied from 233 Wm −2 to 441 Wm −2 , 224 Wm −2 to 431 Wm −2 , 219 Wm −2 to 432 Wm −2 , and 241 Wm −2 to 438 Wm −2 , respectively.during the dry season.Figure 3   the LW d and cloud cover of the four sites over the study period in dry season.LW d in all the four sites showed positive correlation with the cloud cover in wet season; however, this relationship is not as significant as that of dry season because there are only few clear sky days during wet season, as shown in Table 3, while there were more than 20 days of clear sky ( = 0) during the dry season.It can be seen that the cloud cover strongly affects LW d , while in clear sky condition, the LW d had lower values, which dropped significantly and approached its lowest value.This variation is obviously much smaller in wet season than the dry season.

Factors Affecting Downward Longwave Radiation in
Dry Season.The average air temperature and water vapor pressure on cloudy days were observed to be higher than  those in clear sky days.Figures 5 and 6 show the average daily air temperature and water vapor pressure, respectively, at the study sites during the dry season.During the clear sky days, the wetland had the smallest surface albedo (about 0.03∼0.1 for small zenith angle, [26]), which resulted in the highest temperature and water vapor pressure.However, as cloud cover is a kind of albedo (0.6∼0.9, [26]), when combined with the other surface albedo can affect surface air temperature.Thus the agricultural area shows the highest temperature and water vapor pressure in cloud days.This could be explained by the fact that under cloudy condition, albedo of soils and vegetation are decreased thus resulting in higher temperature and water vapor.High albedo of the rangeland area (0.26, [26]) resulted in low temperature and low water vapor pressure under all-sky conditions.
Figure 7 shows the LW d from four different land use sites in the dry season with the largest on the urban area and the smallest on the rangeland area in both clear sky and cloudy conditions.Considering the effect of outward longwave radiation (LW o ), which is the solar radiation absorbed by the earth that causes the planet to heat up and emit radiation, it can be observed that the agriculture area had the largest LW o while rangeland area had the smallest LW o .Figure 8 compares LW o and LW d on the four different land use sites in dry season, while Figure 9 shows the ratio of LW d to LW o .Because under clear sky condition a significant fraction of the longwave radiation emitted from the surface is absorbed by trace gases and suspended particles in the air, therefore, the urban area had the largest value of LW d /LW o , compared to the other three land use areas.This condition results in atmospheric greenhouse effect.
Also in Figure 6 the relationship between water vapor and LW d under clear sky condition suggests that though the water vapor in the urban area was lower than the other areas but LW d was larger.This suggests that (1) the geometry of city streets absorbs more shortwave radiation and makes longwave radiation be exchanged between buildings rather than lost to the sky, (2) the concrete structures especially paved roads as well as the high density of industrial processes in the urban environment are favorable for pollution and dust release, and (3) longwave radiation trapped in the polluted urban atmosphere leads to the urban greenhouse effect [27].

4.3.
All-Sky   Model Calibration for Dry Season.In this section, the general form of land use-adapted model, equation (4) was used in developing all-sky LW d at the land use sites in the dry season.Clear sky data obtained from CNR1 were used to determine the coefficients for LW dc in (2a) and (2b).Using observed data for all-sky condition during dry season and (2a) and (2b) with cloud cover data the coefficients and were determined from (4) for all land use areas as shown in (e) through (l) (Table 4).In Figure 10 the new all-sky LW d model is verified by comparing LW d data obtained from measurements over the study area.The results show that the new all-sky LW d models closely predict the measured data with  2 values between 0.88 and 0.92 for all land use areas studied.These models were compared to four existing models for all-sky conditions [7,8,12,20] as shown in Table 5.The new and existing modes used (2a) and (2b) for calculating LW dc , and in the Rizou and Nnadi' study [15], they proved that land use adapted LW dc had the better statistical performances than the existing models, including Jacobs [8], Maykut and Church [7], Sugita and Brutsaert [20], and Duarte [12].Statistical evaluation of the performance of these models suggested that the new all-sky model gave the smallest values for the BIAS, RMSE, MAE, and PMRE (Table 5).Amongst the four existing models, Jacobs's [8] model had the best performance on the rangeland area but the worst on the urban area, while Maykut and Sugita's model had the best performance on the urban but the worst on the rangeland area and Duarte's [12] model had the worst performances of the four different land use areas.
In validating the new all-sky models, an agricultural land use area under all-sky conditions at Bondville, Illinois, was selected.The new agricultural land use clear sky model (Equation (k) in Table 4) was used to determine LW dc and the cloud coverage data was obtained from the nearest NOAA station, located at Champaign/Urbana Willard Airport, while equation (l) was used to calculate all-sky LW d .Figure 11 shows that the new all-sky model had a very good fit with the data with  2 value of 0.93.The four existing models were also compared to the observed data from Bondville, Illinois.The statistical results show that these models performed poorly as shown in Table 6.The poor performance could be attributed to the fact that these models did not consider effects of land use in their development.Hence, land use is an important factor in developing all-sky LW d .Figure 2 and Table 3 show that, in the wet season, the LW d was higher with much fewer days of clear sky compared to the dry season.The fact that there was only one or no clear sky day at all the four sites during wet season indicates that it was unnecessary and impossible to calculate the LW dc accurately.However, LW dc is needed for the calculation of LW d under all-sky condition, as shown in (4).In order to overcome this difficulty, the initial approach was to substitute the values of temperature and water vapor in wet season into dry season model under clear sky condition to come up with LW dc and then substitute in the LW d model to generate wet season model under all-sky conditions using (4).The statistical results of this analysis are presented in Table 7.It can be seen that the errors were higher than those obtained in dry season condition.

4.4.
All-Sky   in Wet Season.Another approach was proposed in this study where a term called pseudo-LW dc was introduced.The pseudo-LW dc is defined as a longwave radiation value during wet season when the cloud coverage equals a certain cut-off value that is small enough but can assure enough observation data for the regression of (2a) and (2b), for example, 10 percentile of the whole observation cloud coverage data such that (4) would be applicable to cases where cloud coverage is larger than the cut-off value for the pseudo-LW c .In this study, a cut-off cloud coverage value of 0.1 was used to define the pseudo-LW dc giving clear sky days in the observed data to be 22, 24, 30, and 39 days for agriculture, rangeland, wetland, and urban area, respectively.The all-sky LW d models for wet season generated based on pseudo-LW dc are given in equation (m) through (t) for all land use areas considered as shown in Table 8.
The results and the statistical analysis are presented in Figure 12 and Table 9, respectively.The statistics by the new model following the pseudo-LW dc approach gave the smallest values when compared to the existing four models as shown in Table 9, therefore suggesting that this approach provided a better prediction except for the agricultural area.The discrepancy could be attributed to improper selection of the cut-off value of cloud coverage for the pseudo-LW dc .As addressed above the modified equation ( 4) is mainly  applicable when the cloud cover is larger than the cut-off value.As shown in Figure 4, Lindsey Citrus site has fewer days with cloud coverage larger than the cut-off value in wet season; hence, the amount of data used to estimate pseudo-LW dc is limited, which in turn affected prediction ability of LW d .Hence, sites with more days with cloud have better prediction.use.Since different land use has different albedo in relation to energy and water budget, the effects of temperature and water vapor pressure on various land use were evaluated using the albedo.The results of the analysis suggested that (1) the wetland area had the smaller albedo resulting in the higher temperature and water vapor pressure in the clear sky condition, whereas the rangeland had the higher albedo leading to lower temperature and water vapor pressure in allsky conditions and (2) the LW d at the four sites investigated varied with larger values in the urban area and smaller value in the rangeland land in both clear and cloud sky conditions.Based on the seasonal variation dry and wet season data were separated and used for developing LW d models for different land use under all-sky conditions.This approach enhanced the models suitable for dry season and wet season prediction.The dry season models for the land use areas investigated performed better than existing models for LW d under all-sky condition as indicated by the statistical analysis of the results.However, the wet season models did not do as well as the dry season models.The low performance of the wet season models could be explained by the presence of one or no clear sky day condition at all the four sites, which made it difficult to calculate the LW dc accurately; therefore, developing a wet season model for LW d was challenging.To overcome this difficulty, a term, pseudo-LW dc , was introduced to replace LW dc in all-sky model ( 4).This

Figure 1 :
Figure 1: Location of the CNR1 and weather stations in the SJRWMD region.

Figure 3 :
Figure 3: LW d and cloud cover during wet season.

Figure 4 :
Figure 4: LW d and cloud cover during dry season.

Figure 5 :Figure 6 :
Figure 5: Average daily temperature in dry season.

Figure 9 :
Figure 9: Ratio of LW d to LW o in dry season.

2 ) 2 )Figure 10 :
Figure 10: Comparison of new LW d models for all-sky and observed data in dry season.

Figure 11 :
Figure 11: Validation of all-sky LW d at Bondville, IL.

Table 1 :
Existing LW d model for all-sky condition.

Table 3 :
Comparison of LW d and cloud cover days in wet and dry season.
presents the LW d and cloud cover in the four land use sites during wet season, while Figure4provides Figure 7: LW d of different land use sites in the dry season.
) LW o of clear day (W/m 2 ) LW o of cloudy day (W/m 2 ) Figure 8: LW o in dry season.o * 100 (%)

Table 5 :
Comparison of model predictions with observed all-sky LW d data in dry season.

Table 6 :
Statistical analysis for model verification and validation.

Table 7 :
Statistical performance of the LW d dry season models tested for wet season.
Analysis of the observed LW d data in 2004 showed seasonal variation on different land use, suggesting that LW d have higher values and are stable during wet season and lower values with relatively large variation during dry season.Because of the variation in the dry season, the LW d data was used to compare factors affecting LW d radiation such as temperature, water vapor pressure, cloud cover, and land

Table 9 :
Comparison of model predictions with observed all-sky LW d data in wet season.