
Boundary layer parameterization for Finnish regulatory dispersion modelsAri Karppinen, Sylvain M. Joffre and Pentti Vaajama Abstract
1. Description of the FMImeteorological preprocessorThe parameterization schemes used in the dispersion models of the FMI are based on the energy flux method of van Ulden and Holtslag (1985), where the turbulent heat and momentum fluxes in the boundary layer are estimated from synoptic weather observations. The basic concepts of the parameterization are given below. 1.1 Basic scaling parameters The first important scaling parameter is the friction velocity u_{*} , which determines the shear production of turbulence kinetic energy at the surface. According to surfacelayer similarity theory we have a relationship between the measured wind speed at height z and the friction velocity: (1) where z_{o} is the roughness parameter and for the stability function we use , for L<0 and , for L>0 The turbulent heat flux H_{o} at the surface and the friction velocity determine together the second important parameter, a temperature scale (2) where is the air density and c_{p} is the specific heat capacity of air. The third important ABL scaling parameter is the MoninObukhov length scale L defined by (3) where T_{2} is the air temperature at the height of 2 m , and k is the von Karman constant ( k = 0.4.). If the primary parameters to be evaluated are zo, u_{*}, and h, all other parameters can be estimated as functions of these four 1.2 The surface heat fluxThe basic parameter governing the stability and turbulence production in the boundary layer is the surface turbulent heat flux H_{o} . In a stationary and horizontally homogenous boundary layer the balance of the turbulent energy at the surface is given by (van Ulden & Holtslag, 1985) : (4) where is the latent heat flux, Q* is the net radiation flux and G is the conductive heat flux to the ground. The latent heat flux is estimated by applying the linearized saturation curve and the surface energy budget (5) where S is the slope of the saturation specific humidity curve, is the latent heat of vaporization for water and is an empirical temperature scale ( = 0.033 K, according to de Bruin & Holtslag, 1982). The parameter is a function of the surface moisture (Priestley and Taylor, 1972) and it gets values in the range 0.5 1 according to following table: Table 1 Values of moisture parameter in the FMI model .
Parameter S is a function of temperature : S = 51371.0 exp( 5423.0 (1/273.16  1/T_{2}))/ T_{2}^{2} . Using the equations given above the temperature scale (=  H_{o} / c_{p}u_{* }) can be written as (6) 1.3 The surface radiation budgetEquation (4) contains the net radiation flux Q* and G ,the conductive heat flux to ground, both quantities not routinely observed. The net radiation parameterization in the FMI model is basically that of van Ulden and Holtslag (1985) and unless otherwise stated all the following equations and values of parameters are based on that report. The equation for the net radiation reads (7) where Q_{i}* is the radiation flux in an isothermal atmosphere, and Q* is the deviation from this in the real atmosphere. This deviation is evaluated as a function of the difference between air temperature T_{r} at a reference height z_{r} = 50 m and the surface radiation temperature T_{o} (8) The parameter is the StefanBoltzmannconstant (=5.67 10^{8}W m^{2} K^{4}). The temperature difference T_{r} T_{o} will be explicitly calculated later. 1.4 The incoming shortwave radiationThe net radiation for an isothermal atmosphere Q_{i}* is evaluated from the net incoming shortwave radiation K* , the net longwave radiation L_{net} =L_{in}Lout and the incoming longwave radiation of the clouds L_{c}: (9) Q_{i}* = K* + L_{net} + L_{c} At high latitudes the net radiation at the surface correlates better with the sunshine duration than with the cloud cover . Thus, in the FMI model, K* is a function of the incoming net radiation flux at the surface R_{S }and (10) K* = (1r) R_{S}(K_{R}) where r is the surface albedo and R_{s} is a function of the observed hourly sunshine time and K_{R}. The clear sky radiation part (K_{R}) is a function of the solar elevation angle (11) where I_{o} is the solar constant (1372 W/m^{2}). The effect of clouds is incorporated in a regression equation based on the records of hourly solar radiation and sunshine amount from the Jokioinen observatory in Southern Finland. The regression equation reads (12) where R_{SS} is the observed hourly sunshine time. The empirical constants refer to a ten year period (196574) at Jokioinen. 1.5 The outgoing and incoming longwave radiationThe outgoing longwave radiation L_{up} of the surface is a function of the surface radiation temperature T_{o}. In isothermal atmosphere this unkonown temperature can be replaced by temperature at reference height T_{r}. With this replacement the equation for L_{net} reads (13) where is an empirical constant. The contribution of the incoming longwave radiation from the clouds to the radiation budget is parameterized by a regression equation. The cloud black body radiation is defined through the equation (14a) , The cloud base temperature T_{c} is evaluated assuming an adiabatic lapse rate between the surface and cloud base: (14b) T_{c} = T_{2} +_{d}Z_{c} where _{d} =  0.01 C^{o}/m and Z_{c} is the cloud base height derived from observations. The total amount of dominant clouds C_{c} is the sum of the amount of low and middle cloud. The contribution of high clouds to the surface radiation budget is considered negligible, especially when there are several cloud layers. It has been assumed above that in presence of low clouds the boundary layer is nearly neutrally stratified and, in contrast to the shortwave radiation, the longwave radiation part is not a function of the temperature difference T_{r}T_{o}. To account for the annual cycle in albedo, the regression method was applied separately for winter and summer. The following regression equations based upon the ten years period 196574 from the Jokioinen radiation records were obtained for Finnish conditions (Vaajama, 1989) : For summer (defined here by the absence of snow cover) (15a) L_{c} = 0.64 L'_{c} and for wintertime (ground covered by snow) (15b) L_{c} = 0.56 L'_{c} The ground heat flux G still remains to be parameterized. This flux is evaluated as a function of the difference of the air temperature T_{r} at the reference height and the surface radiation temperature T_{o} (16) where A_{G} is an empirical constant ( 5 Wm^{2} K^{1} ). Again, there are no routine observations of the radiation temperature T_{o}. In this case the errors caused by using the screen temperature T_{2}, would be significant. However, the value of (Q*G) can be computed from the set of equations (4)(6) simultaneously with equation (16) with the other boundary layer parameters. This is actually one of the main advantages of the van UldenHoltslagmethod. For unstable boundary layer (L < 0) we use the fact that Q* is strongly correlated with Q* : (17) Q*=  A_{H}Q* where A_{H} is an empirical heating coefficient estimated from 10 year radiation measurements at Jokioinen observatory From equations (7),(8),(16),(17) now follows (18) For stable boundary layer (L<0) it follows from equations (7) and (8) that (19a) . and the temperature difference which is now strongly affected by wind speed is estimated from the potential temperature profile equation: (19b) where z_{0h} = 0.03 cm for the temperature roughness height for heat and z_{r }= 50 m have been assumed. This completes the parameterization for the difference (Q*  G) and we have now an estimate for the temperature scale as a function of the friction velocity u_{*} and the MoninObukhovlength L. Together with equations (1) and (3) we can solve the 3 parameters L, u_{*} and by iteration. 2 Comparison of the FMImethod to the Berkowicz/Prahm scheme2.1 Net radiation estimationsFMImethod divides the net radiation to three parts: shortwave radiation from sun , blackbody radiation from clouds and ground and longwave radiation of (isothermal) atmosphere. Shortwave radiation is approximated by a regression equation which uses observed hourly sunshine time as the explaining variable in the regression model. The radiation from clouds is modelled by another regression equation , which uses the total cloudiness and cloud height as explaining parameters. The Berkowicz/Prahm method uses two regression models (one for daytime and one for nighttime) which use the synoptic measurements of cloudiness as the most important explaining variables. The net radiation estimates of these two schemes is illustrated in figures 1 and 2
Figure 1. Daytime net radiation estimates by FMI and Berkowicz/Prahm preprocessor models.
Figure 2. Nighttime net radiation estimates by FMI and Berkowicz/Prahm preprocessor models. 2.2 Partitioning of the energy The methods have one basic difference in the energy partitioning scheme. As the Berkowicz/Prahmmodel (Berkowicz and Prahm,1982) evaluates the resistances ra and rc and humidity deficit in a quite complicated way the FMImodel utilizes the modified PriestlyTaylor model (van Ulden and Holtslag, 1985) which divides the evaporation in a part which is strongly correlated with (Q*G) and a part which is not correlated with the equalibrium evaporation. That leaves us with only two empirical parameters to be evaluated (see eq. 5) in the FMImodel. The surface and soil moisture are estimated differently in the models. The FMImodel uses synoptic weather codes and amount of rain to estimate the surface moisture and the PriestlyTaylor parameter a (see table 1). The Berkowicz/Prahm.model uses accumulated net radiation for the measure of the soil moisture. These estimates are not directly comparable as the partition schemes and use of these moisture estimates differs in these two models. 2.3 Statistical comparison of the outputs of the two models As the two methods differ quite a lot in the details of parametriazation it was extremely difficult to compare the models without actually doing some calculations with the models using identical synoptic data for the input of the two models. At the end of year 1995 FMI got the code of the OML Meteorological preprocessor (Olesen and Brown, 1992) from the National Enviromental Research Institute (as a part of larger cooperation in the airquality modelling between FMI and NERI). The basics of this OML model are essentially identical to those used in the SMHImodel so this OML preprocessor was suitable for continuing the comparison studies and estimating the performances of the models against each other with some real synoptic data. The period chosen was 10 years from 1983 to 1993 , but the preliminary results presented here cover only the first year 1983. The meteorological data used is collected from southern Finland and the only preparation mede before using the synoptic data for the input of the preprocessors was an interpolation form 3 hour measurements to hourly values. 2.3.1 Comparison of the net radiation and turbulent heat flux
Figure3. Quantilequantile plot of net radiation estimates of FMI and OMLmodels. The figure 3 suggest strongly that in practice (in statistical sense) the estimates of net radiation by these two models give very similar results. The plot of the cumulative distributions of turbulent heat flux estimates of these two models is presented in figure 4 , which shows that the energy partitioning schemes compared differ quite a lot, not only in the parametrisation details but also in the resulting turbulent heat flux estimates.
¨Figure 4. Quantilequantile plot of estimates of sensible heat flux. There is one obvious similarity in the estimates : the ratio of number of stable vs. number of unstable situations is roughle equal for these two models. In the stable side the OMLmodel gives consistently more negative enrgyflux values than the FMI model. In the unstable side the FMImodel gives larger values for turbulent heat flux than the OMLmodel. These results (althought based on only one year data so far) suggest that these two paramerization schemes divide the available energy differently between the latent and turbulent heat fluxes althought the basic input is identical and net radiation estimates are nearly identical. 2.3.2 Comparison of the MoninObukhov lengths For the Monin Obukhov lengths a straigthforward comparison is not very instructive. Instead the MOlengths should be used for stablity classification and a comparison between the frequencies between these classes could be made. At this stage however such a classification is not yet made so a simple density distribution of the inverse MOlengths produced by these two models is presented.
Figure 5. Density distribution of the inverse MoninObukhov lengths. There is one important difference between these two figures: the OMLmodel limits the growth of 1/L in the stable side , which makes the distribution function quite symmetrical around the neutral (1/L small) area. Ther is no such a limit in the Finnish model , which produces quite a many “superstable” situations. This is a very important difference for the air quality modeller as these very stable situations are often connected with airpollution episodes. So it is of highest importance to be able to paramerisize these situations correctly. 3. Comparison with measurementsWithin the COST710 action a comparison between measurements and parametrization models is made and reported by Johansson, 1996 In FMI there are several measurementcampaigns (Walden et al., 1995, Härkönen et al., 1996) which produce data suitable for similar comparison studies. As an example of the behaviour of the FMImodel against the measurement data a comparison between the measured (mast measurements of wind at heights 2,5and 10 meters) and modelled friction velocity is given in figure 6.
Figure 6. Friction velocity: FMI parametrization model vs. local measurement. 4. ConclusionsThe preprocessor of metorogical data used Finland is described and compared to a similar scheme which is in use in Sweden and Denmark. The physics behind these preprocessors is nearly identical. The measurements used in these schemes are slightly different. Estimation procedures for net radiation differ quite a lot but the results (at least statistically) are nearly identical. The partitioning schemes vary quite a lot and also the results of parametrization differ significantly especially in the stable regime. At the moment synoptical data only for one year has been used for the statistical analysis. After the analysis for the whole 10 year period is finished final conclusions about the performance of these two models (parametrizations) against each other can be stated. The comparison of the paremetrization schemes against the measurements is on the way. The main difficulty in these comparison is the availability of good quality measurement data. We believe that the measurement campaigns at FMI will produce data which could be used for these comparison studies in the near future. 5. References Berkowicz, R. and Prahm, L. P.,1982. Sensible heat flux estimated from routine meteorological data by
resistance method. J. Appl. Meteor. 21, 18451864 . Karppinen, A., Kukkonen, J., Nordlund, G., Rantakrans, E., and Valkama, I., 1996. A dispersion modelling
system for urban air pollution. Finnish Meteorological Institute, Publications on Air Quality. Helsinki, 40 p. (in
print). 