Not Only AUSTAL2000 is Not Validated

On the basis of regulations and directives, since 2002 the particle model AUSTAL2000 has been mandatory in the Federal Republic of Germany for the calculation of the spread of air pollutants. In order to achieve harmonization, other model developments require that the physical basis of the AUSTAL be adopted. However, the author of this paper has variously proved that this dispersion model itself is not verified and therefore not suitable for carrying out propagation calculations. All reference solutions are faulty. Doubtful comparisons and test bills are carried out. So z. For example, 3D wind fields are compared with the rigid rotation of a solid and the position of sources is given in 200m, but their effects cannot be seen in the calculated concentration distributions. The authors of the AUSTAL address these objections with chimerical arguments and questionable definitions of deposition velocities and other dubious calculations of sedimentation and deposition currents. With each attempt to explain deepen the incomprehensibility, and you become entangled in other contradictions. This article describes that deposition currents are to be determined according to physically established laws and cannot be set arbitrarily according to amount and direction. It is shown that soil concentrations are calculated speculatively by the authors of AUSTAL. The definition of the deposition rate is substantiated physically. The author also analyzes by way of example that even further model developments are validated by the faulty reference solutions of the AUSTAL. Not only AUSTAL is not validated. In summary, further contradictions are described. AUSTAL is a further development of the dispersion model for air pollutants LASAT from the year 1984. LASAT is raised by the authors themselves and described as the mother model of pollutant spreading in Germany. For 34 years, faulty model developments have been extensively promoted.


Introduction
Within the framework of the Technical Instructions on Air Pollution Prevention according to [1] TA Luft, since 2002 the particle model AUSTAL2000 in the Federal Republic of Germany has been prescribed as mandatory for the calculation of the spread of air pollutants. To prove its suitability, other model developments must be verified with AUSTAL, which is why u.a. Reference solutions are provided. However, [2] Schenk and [3] Schenk show that all sedimentation and deposition reference solutions are flawed and that all the homogeneity tests described are only useless trivial cases. AUSTAL itself could not have been validated. The law of mass conservation and the II law of thermodynamics are violated. Further contradictions, which are to be justified with the violation of these conservation laws and main clauses, are pointed out.
In [4] Trukenmuller et al. and [5] Trukenmüller disagree and claim that all the objections raised are due to misunderstandings and physically different ways of looking at things. Also, one would like to prove that there is an equivalence between the different specified reference solutions, what u.a. with questionable definitions of the deposition rate. All contradictions would be clarified. However, one does not know that the deposition rate is a material constant and cannot be falsified arbitrarily. However, an obvious contradiction is overlooked in all these explanations. Once one wants to counter all concerns about AUSTAL with physical evidence, but on the other hand one intends to bring about an equivalency to the correct solutions. This contradiction explains why all the efforts of the authors of the AUSTAL to refute the complaints raised in relation to their propagation model are reversed.
In [6] Schenk, the author goes on to deal with these opposite opinions. The mistakes in the derivation of the questionable reference solutions of the authors of the AUSTAL are clarified and corrected. With the help of valid integral equations it is proved that the violation of thermodynamic laws of conservation and law is not limited to isolated cases. It is applicable to all sample solutions that 188 Not Only AUSTAL2000 is Not Validated use the faulty reference solutions. It has also been shown that the equivalence between the two reference solutions allegedly existed by the authors of the AUSTAL cannot exist. The alleged equality is based on a deceptive derivation. Mathematics and mechanics prove that all tasks assuming a "volume source over the entire computing area" are identical and have only one trivial solution and cannot be different. Claiming that sources have been included in 200m will mislead the public. Not a single concentration profile reported by the authors of the AUSTAL suggests the presence of such sources. By means of a root cause analysis, it is clarified that the faulty reference solutions are based on an already in 1984 by [7] Axenfeld et al. can be attributed to a questionable description of all sedimentation and deposition processes. This development is dignified by the authors of the AUSTAL as the mother model of AUSTAL called LASAT.
In [8] Trukenmüller one gets involved in further contradictions. With regard to the deposition one introduces, in addition to the already existing definitions, an additional interpretation. There is now a so-called "true deposition rate", but it is still not recognized that this can only be a material constant. The validity of BERLJAND's relation can recalculate. A propagation calculation is thus completely unimportant. Already during the filling one pays attention to the fact that in each volume of the computing area the same emission is set free, and thus the concentrations are spatially constant. It is also denied that the soil sources are calculated speculatively.
In this article, using the example of case 22a with alleged sedimentation without deposition, in a single case by means of e.g. of the GAUSS integral theorem proves that the law of mass conservation and the II law of thermodynamics are violated and because of an indeterminacy in the calculation equation the soil concentrations have to be determined speculatively. The integral equation used for this purpose is concealed from the public by the authors of the AUSTAL. This article also provides proof that the BERLJAND relationship is physically justified. The same argument is used to define the deposition rate. In many cases, the author of this amount also complained that the erroneous theory for sedimentation and deposition, founded in 1984 according to [7]

Methods and Material
Mathematics and mechanics are used alone as valid methods of incorruptible evidence to conduct subsequent investigations. By means of differential and integral equations, such as The GAUSS integral theorem for the transformation of volume into surface integrals proves that the conservation of mass and the II law of thermodynamics is violated. As further methods fluidic and thermodynamic doctrines are used to the conservation laws of momentum, heat and mass transport. In addition there are foundations of the theory of heat and mass transfer.
As material the publications of [7] Axenfeld et al., [11] Janicke et al., [9] Janicke, [12] Janicke, [13] Janicke., [4] Trukenmuller et al., [5] Trukenmüller and [8] Trukenmüller. The results of these publications are checked for correctness and plausibility using the specified methods and procedures. Further research results which are used concern the works [14] Stefanek, [15] Stefanek et a.l, [16] Schul and [17] Kubica. Figure 1 shows the results of the investigations carried out on the validity of the law of conservation of mass and the II. Law of Thermodynamics using the example of case 22a, sedimentation without deposition.

Deposition Streams are Directed against the Positive Concentration Gradient and Cannot be Determined Arbitrarily by Amount and Right
First, the basic equations used will be explained. The differential equation (01) describes a one-dimensional stationary mass transport in the free atmosphere. The equations (02) and (03) explain the correct solution Environment and Ecology Research 6(3): 187-202, 2018 189 according to [6] Schenk and the faulty reference solution according to [9] Janicke. Equation (02) results as a correct solution of the differential equation (01). The concentration distribution is a function of the sedimentation and deposition rate as well as of the diffusion parameter and the altitude coordinate. K c / z v c 0 ⋅∂ ∂ − ⋅ = , but only by arbitrariness of the authors of the AUSTAL, as can be read in [6] Schenk. The graph of Figure 1 describes the concentration curve after the faulty solution (03). The concentration gradient on the ground is negative, so contrary to all expectations for the spread of air pollutants, a deposition current of 2 11,57 g/(m s) µ ⋅ in the direction of the free atmosphere should result. The contradiction to the II. Law of Thermodynamics is that in the direction of the free atmosphere according to the solution given, a concentration compensation by conduction should take place, but it is stated that it disappears due to lack of deposition with d v 0 m/s = , but what the adjacent concentration gradient contradicts. The specified concentration curve forces an equipotential bonding in the direction of the free atmosphere and cannot be chosen freely in terms of magnitude and direction. Not only by these considerations, the calculated concentration course is doubtful. The given concentration distribution could only be understood if one laid the source in the ground, which in addition to all the absurdity but also the assumption "volume source over the entire area of the law" distributed again would contradict. These relationships are described by equations (04). By applying the GAUSS integral theorem, equations (05) explain that solution Eq. (03) with the "specialization Fc = 0" violates the mass conservation law.
All inconsistencies, which are revealed as a consequence of the faulty reference solutions, could thus be elucidated using the example of case 22a.

For Sedimentation and Deposition, the Soil Concentrations are Calculated Speculatively
Before all the peculiarities of the case 22a, can be further discussed, it should be remembered that according to [9] Janicke and [10] Janicke, all verification tests are divided into two groups. On the one hand, it is homogeneity tests and, on the other hand, it is tests for sedimentation and deposition. Finally, case 21, deposition without sedimentation, case 22a, sedimentation without deposition, and case 22b deposition with sedimentation are described. By c d 0 F v c = ⋅ we mean "the mass flow density forced by the source" or, in the case 22b, a "source strength of . In both these cases, it is possible to proceed in such a way that the deposition velocity is different from zero, d v 0 ≠ .
The emissions amount to 2 c F 1 g/(m s) = µ ⋅ and should have been located at 200m, which could not have been, according to [6] Schenk. Depending on how the source strength c F is determined, without having to use an analytical solution, the soil concentration is already obtained, which is very surprising, at least for the case 22b.
With regard to the calculation of the soil concentration , however, the situation is different in case 22a. Here no deposition should take place, which is why the deposition rate must be assumed to be d v 0 m/s = . This results in the used "specialization 2 c F 0 g/(m s) = µ ⋅ " for this case. It is now the case that no equation of determination is available for the calculation of the soil concentration. This results in an indefinite expression 3 0 This expression makes it possible to arbitrarily set or somehow determine the soil concentration. The appropriate solution function, which one would have had to develop from the relevant differential equation (1), is not suitable because of its erroneous derivation and indeterminacy. It will be of interest how the authors of the AUSTAL proceed. Because of the c "Spezialisierung F 0" = , the erroneous reference in which the soil concentration is the only unknown. To calculate the soil concentration, a further determination equation has to be developed. The simplest case of a disappearing soil concentration is excluded, because otherwise the whole problem of the case 22a would be in question. A solution function based on the differential equation (1) is likewise not available because of the described vagueness, which is why it is necessary to help one another.
In this predicament speculate the authors of the AUSTAL and use the case 11 of the homogeneity test. There, as in all other cases, the same geometrical relations exist for homogeneity, and there already at a total emission of E 100 kg . But because this triviality is contrary to the whole task, one has to rely on a different explanation about the origin of emissions. For this reason, the authors of the AUSTAL use the source form of case 11 "volume source over the entire computing area" distributed. Obviously, the source types are changed arbitrarily by the authors of the AUSTAL as needed. However, in the case of this substitution, one overlooks the fact that the same problem exists for case 22a because of the spatial concentration gradients that vanish here, as in case 11, and that a solution deviating from 3 c 500 g/m konst. = µ = cannot exist at all, as in [6] Schenk was detected. This fact is ignored. As the authors of the AUSTAL now proceed, with means of mathematics and mechanics is no longer explainable. They compulsorily distribute the mass of E 100 kg = in the control room of case 11 so that the new distribution satisfies its erroneous . However, knowing this equation would be necessary if other authors of model developments want to validate their algorithms. This approach is speculative and not physically substantiated. If one compares this with comparisons of procedural mixing, this redistribution would be equivalent to demixing, but this would be understandable only with an energy input, which, however, can not be mentioned here. The conditions can be easily understood using the example of Figure 2. Equations (6) describe the geometrical relationships of cases 11, 13, 14 and 22a. In all cases, it is assumed that there is a "volume source over the entire computing area". The specific source term is The equations (7) explain that all spatial concentration gradients must disappear due to this volume source. The concentration adjustment of  The authors of the AUSTAL calculate the soil concentration speculatively and mislead all model developers and the public.

Deposition Rate and Calculation of Deposition Currents
As mentioned in the introduction, is deposited in the soil. Storage is understood to mean storage and not the opposite of loss. To comply with stationary observation, the sediment must be mechanically removed continuously, e.g. in the case of surface winds and other whirling up. In the example of a procedural exhaust gas purification is comparatively a discontinuous cleaning of filter surfaces. The deposition stream penetrates into the interior of the soil and leads to an enrichment of the soil with the pollutant in question. The model assumes that the soil has an unlimited capacity, which cannot be avoided in a stationary observation. Examples include the penetration of aerosols into the soil or its acidification by sulfur-containing air admixtures. Other examples include the penetration of radionuclides into the subsurface and the consequent enrichment with radioactive decay products. Assuming a limited absorptive capacity of the soil, a transient approach is imperative. In this case, a complete equipotential bonding in the free atmosphere and in the soil will lead to a constant concentration distribution throughout. The compensation time results as a solution of an initial boundary value task, however, the model equation (01) has to be extended by the temporal change of the concentration and by the source term Trukenmüller. The boundary condition is a constant soil concentration and a constant mass transfer between ground-level atmosphere and soil. The constancy of the mass flows explains the equations (12), and the penetration of the pollutant into the soil near the ground is described by the differential equation (13). It is identical to the differential equation (01), but there is no convective flow in the soil, s v 0 = . As a solution, equations (14) and (15) show a linear concentration distribution in the soil, and thus a constant concentration gradient everywhere The equality of the conductive mass flows as a boundary condition is described by Equations (16) using the constant concentration gradient of Equation (15). Assuming that the concentration T c at ground depth is negligible with respect to the soil concentration , c c T 0 >> , we obtain the equation (17), which arises from the requirement of equality of the conductive mass flows at the Bottom limit results. At the same time, the definition of the deposition rate is obtained as the quotient between the effective mass transport coefficient in the soil and a measure of length which characterizes an indefinite soil This definition also justifies that the deposition rate is a material constant. The parameters B K und T depend on the soil conditions on the surface and on the interior of the soil. The deposition rate thus formed is usually determined experimentally. The deposition rate does not result from a parameterization. It is physically based on the equality of the conductive material flows on the ground. The boundary condition is identical to the relationship given in [19] Berljand, Eq. (17). The deposition rate is equivalent to the mass transfer coefficient The correctness of the calculation is confirmed by combining equation (12) for 0 = z with the integration constant . The boundary condition (17) is also substantiated and successfully applied in [14] Stefanek.
As is well known, the product of speed and mass density leads to mass flow. In the case that the velocity is the deposition rate, the result describes a deposition current. If, however, it is a sedimentation rate, this results in a sedimentation stream. The sum of both explains the total mass flow. However, one cannot say the deposition rate and at the same time claim that the result would be the total mass flow, as stated in [8] Trukenmüller. Although it is possible to parameterize a deposition rate as desired, integration constants are not determined from parameterized boundary conditions but from physically justified boundary conditions.
In contrast to this approach, the authors of the AUSTAL lack the second boundary condition as a consequence of a mass constancy at the boundary surface of the Earth's  (23) shown in Figure 3. The authors of the AUSTAL thus use the equation (12). Instead of determining the resulting integration constant by means of the LAGRANGE method, this is unfounded replaced by a deposition current, which will turn out to be deceptive. Equation (12) shows that no sedimentation current should occur, equations (18  This castling is physically unfounded and arbitrary, resulting in a violation of mass conservation. How to do this is explained in detail in [6] Schenk. In the second case, one does the same thing, but fails to recognize that it provides another trivial solution. It turns out that because of no sedimentation velocity can occur, as equations (18) show 0 = s v . In the first case, this swap avoids a trivial solution, but in the second case, the entire original task is called into question again. These and other contradictions constitute the tragedy with which, from 1984 to the present, the entire development of the AUSTAL is connected.

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Not Only AUSTAL2000 is Not Validated In conclusion, it should be noted that equation (01) is an ordinary differential equation of the second order. According to the theory of ordinary differential equations, two integration constants arise in the solution process. Both are to be determined by means of physically justified boundary conditions. If physics is indisputable, there are also undisputed solutions. In the present case, one has a boundary condition with ( ) 0 0 c z c = = , but the authors of the AUSTAL lack a further physically justified rule with which one could determine the second integration constant. One resorts to controversial definitions of the deposition rate and entrenches itself subsequently engrossed in contradictions. With these statements it was shown that the disastrous development of the AUSTAL had already begun in 1984 with the LASAT model. The causes for this were physically justified.
It can be assumed that the differences formulated above for the definition of the deposition rate and for the calculation of deposition currents can be regarded as sufficiently clear.

Validation on Analytical Solutions and Reference Examples
High demands are placed on the development of algorithms for the solution of differential equations of mathematical physics. First, it must be made clear that physically justified model equations are available. The field of fluid mechanics is determined by experimental and theoretical studies on the movement of liquids and gases. Fluids and gases almost one together under the collective term fluids. A distinction is made between compressible and incompressible fluids. The movement of these fluids is described by the NAVIER-STOKES differential equations. They are the basic equations of fluid mechanics. If the fluids are used as carrier media for heat and material, then further balance equations are added. One then speaks of the coupled differential equation system of momentum, heat and mass transport, which finds application in many scientific disciplines adjacent to fluid mechanics. The spread of air bubbles takes place in the PRANDTL layer, which is why fluid mechanics and thermodynamics are primarily concerned with the motion processes in this layer. Because air pollutants are basically transported in a carrier medium, one speaks of a mass transfer equation. When heat is moved so, this is accounted for by the heat transfer equation. In this way, pulse is moved by the NAVIER-STOOKES differential equations. The coupled differential equation system thus described thus accounts for the transport quantities momentum, heat and material. All these transport processes have an analogy in common. It consists in that these transport sizes are moved equally by convection and conduction. They are in a carrier medium, e.g. Air, stored and continue with the flow. This form of moving is called convective transport. Conductive transport describes the balance of momentum, heat and matter through the occurrence of friction, conduction and diffusion.
In some cases, especially with the spread of airborne pollutants, it makes sense to allow the carrier medium to flow, e.g. Air, to calculate separately. Thus, one often differentiates between a flow and dispersion model. In this case, it is neglected to influence the flow through the incorporated admixture of air, because their concentration in comparison with the density of the carrier medium is small in every respect. In any case, it is necessary to make such an estimate depending on the admixture of air. Because of the existing analogy between momentum, heat and matter, one speaks of a uniform and generalized transport equations. With regard to the use of approximation methods, this generalization is of great advantage. It is now the task to find solutions of this differential equation system. A variety of analytical solutions are available for this purpose. They have the advantage that they are exact solutions, with which one can safely study the interaction of flow and, for example, the spread of air pollutants. In general, however, it will not be possible to be able to describe these complicated relationships between flow and propagation by analytical solutions, which is why approximate methods, such as e.g. on numerical algorithms, is dependent. The numerical methods include the analytical solutions and are generalizable applicable. For this reason, one can check the validity of numerical methods on analytical solutions. They provide an important and convincing statement about the usability of the developed numerical algorithms. Even if all criteria, e.g. Stability, convergence and consistency for which the numerical procedure used is met, validation of analytical solutions cannot be dispensed with. This is the only way to be sure of validly describing complex one-or multi-dimensional as well as stationary or transient propagation processes. However, the presence of correct analytical solutions is indispensable. If the analytical solutions are already flawed, validation is ruled out and irrelevant. For this reason, these solutions for flow and propagation are of great importance. You cannot handle it lightly. For example, if one wishes to investigate transient propagation processes, one has to validate the time-dependent algorithm also with transient analytical solutions. It is not easy to state flatly that compensating operations would occur after e.g. Completed 10 days, if a transient analytical solution is not available at all for validation. Modern understandings of the stability of numerical algorithms also assume that this is always guaranteed when it comes to physically justified model equations. Negative conductive model parameters are not physically explainable and generally prevent convergent solutions. When solutions do not converge and programming errors are eliminated, it is a sure indication that model equations or model parameters are being misused. Within the framework of the theory of momentum, heat and mass transfer sufficient stationary and transient analytical solutions can be provided. Examples include simple solutions of ordinary differential equations for sedimentation and deposition, pulsating pipe flow, FOURIER's solutions for heat transfer, Bessel functions and GAUSS distributions for the propagation of air pollutants, the flow near oscillating walls as well as the flow between rotating cylinders. Other other examples are described extensively in [21] Schlichting, [22] Truckenbrodt, [19] Berljand, [23]  Reference has already been made to the importance of stable numerical methods. The authors of the AUSTAL themselves write that solutions cannot converge. This information raises legitimate doubts about physics, which AUSTAL uses to model propagation processes. It is due to the nature of unstable numerical methods that these divergences can only occur for a short time. However, after any instability that has occurred, the calculation will continue with an error that has occurred. It comes to a fault continuation, where in the end it is difficult to judge what you have received for a solution. The sedimentation and deposition reference solutions given by the authors of the AUSTAL and all homogeneity tests are flawed and not suitable for validation. It is deceptively claimed that the solution was validated on 3D wind fields. In fact, one uses the rigid rotation of a solid. The authors of the AUSTAL lack the idea that one could at least use the EKMAN spiral known in meteorology. By forming integral averages, e.g. with the BERLJAND profiles, faulty solutions are smoothed out. Nevertheless, the error deviations are still up to 70%, which increase even further with a reduction in the source distance. Bessel functions are calculated incorrectly. It is reported by users that AUSTAL also calculates concentrations within closed borders. One explains this incomprehensibility with the fact that particles cannot see house walls, but want through. Such phenomena are more indicative of programming errors than equipping pollutant particles with vision. These and other differences, as described for example in [2] Schenk and [6] Schenk, prove that AUSTAL could not be validated.
Already for the mother model LASAT deposition does not mean storage but loss. The intention was to achieve a harmonization of all propagation calculations, which means that all further model developments have to use the same model fundamentals. For this reason, [18] VDI 3945 publishes reference solutions and other procedural principles, and requires all model developers to validate their algorithms against these dubious foundations and erroneous reference solutions. But as already described, all reference solutions and homogeneity tests are flawed.
The situation is now to be assessed in such a way that most model developers understandably rely on the published rules for validation and verify their algorithms. They respect the authority of the clients of the AUSTAL and rely on credibility. In any case, model developers prove that their algorithms are equivalent to those of the AUSTAL, as shown in Figures 4 and 5, for example.
In both figures, the graphics on the left show the results of the erroneous reference solutions according to AUSTAL for the individual case examples, and on the right, according to [27] N.N., for example, shows the corresponding graphics of an engineering office. As can be seen, the AUSTAL solutions show a satisfactory agreement, which proves that this model development is also flawed and not suitable for carrying out dispersion calculations. While Figure 4 describes all tests for sedimentation and deposition, Figure 5 is all homogeneity tests.
The above statements show that other propagation models have also been validated against the erroneous reference solutions of the AUSTAL. Not only AUSTAL is not validated.
The authors of [4] Trukenmüller et al. provide information. However, there are also propagation models of engineering firms which meet all requirements, but must subsequently validate themselves against the faulty reference solutions of the authors of the AUSTAL. How to do this is easy to recognize.