According to the “Warsaw” scenario, most private farms in the milk areas of Ostroleka Area suffered from a shortage of uncontaminated feed from last year’s harvest and the diet of milk cattle partially included freshly harvested contaminated green feed. Green fodder was included in the milk cattle diet only at half of farms on average for the period from 1.05.86 to 20.10.86.

The data on gross milk production, the forage lands structure, as well as data on ¹³⁷Cs fallout densities and rains for the major fallout period calculated from weather station data are presented in scenario for Warsaw Area and Ostoleka Area.

This information, as well as the calculated data of the dependences on rains of cultivated pasture grass specific activity during the main fallout, given in (Vlasov et al. 2023), were used to estimate the relative proportions of contaminated milk in the milk counties (${\delta }_{milk}^k$) in which its ¹³¹I specific activity was measured. Estimates of ${\delta }_{milk}^k$ for the k-th district were carried out according to the following ratio:

${\delta }_{milk,j}^k\left(R_j^k\right)=\frac{\left[I_{inh,j}^k+{\delta }_{diary}^k·I_{grf}^k\left(R_j^k\right)\right]}{\left[I_{inh,j}^k+I_{grf,j}^k\left(R_j^k\right)\right]}$, (1)

where

j is the calculation model: 1 – direct calculation, 2 – inhomogeneous cloud, 3 – homogeneous cloud;

${\delta }_{diary}^k$ – the farms fraction in the district that does not have stocks of clean feed in May 1986, it is assumed that it corresponds to the average proportion of contaminated feed in the diet of cattle in the dairy district,

${\delta }_{milk,j}^k$ – the radioactive fraction of milk produced in the milk county,

R^k_j – average rains for the rains major period used in the j-th calculation model, mm;

I^k_inh and I^k_grf – ¹³¹I specific activities integrals in milk due to inhalation and contaminated green feed, (kBq/kg)*day;

here

$I_{inh,j}^k=I_{inh,j}^0·\left\{\begin{array}{c}\frac{kC{l}_{j=2}^k}{kC{l}_{j=2}^0}\\ 1,j=1,3\end{array}\right.$, (2)

$I_{grf,j}^k\left(R_j^k\right)=Q_{grf,j}^0\left(R_1^0\right)·\frac{q_{grf,j}^{max}\left(R_j^k\right)}{q_{grf,j}^{max}\left(R_{j=1}^k\right)}$, (3)

where

kCl^k_j is the conversion coefficient of the ¹³¹I specific activity in the atmosphere for the j-th model;

kCl ⁰ _{j =2}, I⁰_inh and Q⁰_grf,j were estimated using the direct calculation model for the Warszawa Observw Astr weather station with rains over the period of major fallout, 0.8 mm; respectively, equal to 1.72 , 14.4 (kBq/kg)*day and 696 (kBq/kg)*day; R^k_j – rains in k – milk county, мм.

An example of the radioecological parameters calculation results for the Warszawski Zachodni milk county with the farms proportion without pure feed stocks by the date of the accident equal to 30% is shown in Table 2.

The data in Table 2 and similar results for the other counties show that the specific milk activity integral due to inhalation is 35–40 times less than due to green feed. Accordingly, the radioactive milk fraction in them does not essentially depend on the calculation model. It does not significantly differ from the proportion of farms without stocks of pure feed by the date of the accident.

The results of calculations for other counties in which milk samples were taken for radiometry, shown in Table 3, demonstrate that in the Ostroleka district cattle were fully provided with stocks of pure feed from last year’s harvest. Therefore, the contaminated milk fraction in this county is equal to the inhalation component fraction in the total activity in milk. According to the simulation model estimates its value is 2%. In Table 3, together with data on the values ${\delta }_{diary}^k$ and ${\delta }_{milk}^k$ the”Warsaw” scenario data on the ¹³⁷Cs fallout densities structure in the counties, rains meteorological data during the major fallout period and the number of ¹³¹I activity measurements in milk at its reception points are also given.

The ${\delta }_{milk}^k$ values were used to adjust the calculated $Q_{cor,j}^{C,k}$ and reconstructed “instrumental” data $Q_{cor}^{M,k}$ of ¹³¹I specific activity in milk in the k-th milk county according to instrumental data for the district k0 to the ratios (4) and (5):

$Q_{cor}^{M,k}\left(t\right)=Q_{inh}^{C,k}\left(t\right)+{\delta }_{rad}^k·\left[Q_{grf}^{M,k0}\left(t\right)-Q_{inh}^{C,k0}\left(t\right)\right]·\frac{\max \left[q_{gr}^{C,k}\left(t\right)\right]}{\max \left[q_{gr}^{C,k0}\left(t\right)\right]}$, (4)

$Q_{cor,j}^{C,k}\left(t\right)=Q_{inh,j}^{C,k}\left(t\right)+{\delta }_{rad}^k·{\delta }_{grf}^k·Q_{grf,j}^{C,k}\left(t\right)$, (5)

were

M and C indexes refer to instrumental and calculated data;

j-calculation model;

Q^k_j and Q^k_cor,j – direct and adjusted dependences of specific 131I activities in milk;

$q_{gr}^{C,k}$ – calculated data of ¹³¹I activity dynamics in pasture grass;

Q^k_inh,j и Q^k_grf,j – calculated dependences of inhalation and food components of milk contamination;

δ^k_grf – corrections for discrepancies of calculated and reconstructed “instrumental” data of specific ¹³¹I activities in pasture grass (Vlasov 2013a).

It should be noted here that the range of coefficient values

$K_{cor,j}^k=\frac{\max \left[Q_{cor,j}^k\left(t\right)\right]}{\max \left[Q_j^k\left(t\right)\right]}$ (6)

for recalculation of ¹³¹I activity in milk instrumental data K^k_cor,j according to the direct calculation models of (j = 1) and homogeneous cloud (j = 3) is equal to (0.95–1.05), for heterogeneous cloud (j = 2) is equal to (0.5–1.7).

According to “Warsaw” scenario, the complete clean feed provision was only in the Ostroleka Area county of the Ostroleka Area and on the Falenty Duze diary farm of the Warsaw Area (Table 3). The largest proportion of contaminated milk (90%) was in the Szczycienski county of the Ostroleka Area. On average, in all districts with ¹³¹I in milk radiometry, the contaminated milk fraction in the WarsawArea area was 2–3 times less than in the Ostroleka Area. Taking into account that the parameters of the ¹³⁷Cs fallout densities distributions in these area in these areas practically coincide. These data may possibly explain the peculiarity of the ¹³¹I milk activities instrumental data presented in Fig. 3.

The most detailed, more than 10 times, multiple instrumental data on the ¹³¹I activity in milk dynamics in the Ostroleka Area counties were obtained for the Ostroleka diary farm, Przasnyski diary, in the Warsaw Area for the Warsaw town diary farm, Legionowski county and Falenty Duze diary farm (Fig. 3).

Note the significant irregularity of the instrumental data for all districts in the all area near their maximum values and the apparent inconsistency between the Fig. 2, Table 2 data and Fig. 3 for the Ostroleka Area.

Firstly, the instrumental data in Fig. 3 for this district, the only one in the Ostroleka Area with 100% provision of clean feed (Table 1), have the same features with the measurement data in all other districts of this area. In all these districts, the provision of clean feed was only partial, and the contamination of milk in them was mainly due to the consumption of contaminated grass pastures.

Secondly, the ¹³¹I milk activity at the Falenty Daze farm at the time of the end of the fallout main was 10 times less than in the Ostroleka Area milk county.

This cartographic data is more consistent with the form of instrumental data on the ¹³¹I milk activity dynamics for this district, which completely coincide with the form of the Przasnyski district data in Fig. 3b with the value δ_diary equal to 80%.

According to the cartographic data of the “Warsaw” scenario (Fig. 4) in the Ostroleka district, the value of δ_diary was (0.5–0.8).

Considering these discrepancies in the Ostroleka area, an additional test was conducted for this area, in which the average proportion of contaminated feed was found to be 60%.

The ¹³¹I milk activities dynamics calculations were carried out for counties for which in the “Warsaw” scenario multiple instrumental data are available. At the first stage, for the Warsaw Area, the following calculations were carried out sequentially for all three variants of input data on rains and ¹³⁷Cs and ¹³¹I activities in the atmosphere:

• calculation without corrections (Fig. 4a – direct calculation);
• calculation which was carried out considering the discrepancies of the calculated and reconstructed “instrumental” green feed ¹³¹I activities (Fig. 4b);
• calculation was performed taking into account the share of pure green feed in the diet of cattle in dairy districts (calculation taking into account adjustments for pollution and relative shares of farms (%) in dairy districts that do not have stocks of clean feed, Fig. 4с)
• calculation that was performed taking into account the amendments of paragraphs 2 and 3 (Fig. 4d).

The results of calculations and instrumental data of milk ¹³¹I specific activities are presented for the Falenty Duze farm and Legionowski county without considering the corrections in Fig. 4a, b for the same district, considering the adjustments for contamination and the contaminated feed fraction in the diet of cattle.

Reconstruction of the inhalation component of ¹³¹I intake into milk had performed on the example of instrumental data for Falenty Duze farm whose cattle diet included only pure feed from the last year harvest. It shows that the calculated data on the homogeneous cloud model are quite satisfactorily consistent with instrumental data both according to the statistics of their relations and their form reflecting the details of dynamics of ¹³¹I volumetric activities in the atmosphere.

The data in Fig. 4 show that the models of direct calculation and homogeneous cloud give almost the same calculated results. This data has 2.5 times better consistency with the instrumental data than the model of heterogeneous cloud. Moreover, the ratio of calculated data to instrumental ones for their entire series is closer to 1 than in the region of their maximum values. This is probably due to the significant irregularity of the instrumental data near their maximum values.

The dynamics of the ¹³¹I specific milk activity in the Ostroleka county studies were carried out, as for the WarsawArea, using three calculation models and in two variants of ¹³⁷Cs and ¹³¹I atmosphere volumetric activity dynamics:

• direct instrumental data of the “Warsaw” scenario obtained in Warsaw city,
• reconstructed “instrumental” data equal to direct instrumental data multiplied by the ratio of the ¹³⁷Cs “dry” fallout calculated density, estimated in (Vlasov et al. 2019b) from direct instrumental data of its activity in the atmosphere, to its minimum instrumental fallout density.

Instrumental and calculated time dependences of milk specific ¹³¹I activities in not taking and taking into account adjustments for contamination and the pure feed part are presented in Figs 5, 6 of Ostroleka and Przasnyski counties. As well as in Fig. 7 in the form of average geometric calculation/measurement ratios histograms for instrumental data of all their series and in their maximum values area.

In (Vlasov et al. 2020a) when creating a mutually agreed database of input data was discussed the variant with the recalculation of specific volumetric activity ¹³⁷Cs and ¹³¹I in the atmosphere over the Ostroleka area. In (Vlasov et al. 2023) this option was further considered in studies of grass pastures contamination dynamics. A comparison of the data in Fig. 5a, b shows the validity of using this variant.

This is confirmed by a better consistency of the calculated and instrumental data of ¹³¹I activities in milk in the counties of the Ostroleka Area than in the variant with their direct instrumental data.

Note that the instrumental data for the Przasnyski in Fig. 6 county have a more regular appearance without a dip in the area of 12–18 days, as in the county Osrtoleka in Fig. 5.

The analysis of the calculated and instrumental data comparison showed that the calculated data for Warsaw Area reproduce the instrumental data better after 30 days than for Osrtoleka Area, and worse for times less than 20 days. There is an almost completely satisfactory consistency of the calculated and instrumental data in the range of 20–30 days for both variants.

The improvement in the convergence of calculated and instrumental data with sequential accounting of corrections is characteristic both for all districts of both districts, and for these milk areas in whole (Fig. 8).

Note the main features of the residual errors of the calculated and instrumental data in Fig. 8:

• sequential consideration of corrections leads to an improvement in the convergence of the residual errors to 1, in all three calculation variants;
• the ratio of calculated to instrumental data with recalculated ¹³¹I activities in the atmosphere of the Osatroleka Area is on average 0.25–0.3 closer to their ideal value of 1 than in calculations with direct cloud data, for all calculation variants;
• the ratio values for a series of instrumental data in the area of their maximum values are 30% greater, than for their entire series;
• the residuals for the Warsaw Area are 0.2–0.2 5 closer to 1 than for the OstrolekaArea area, in all variants of accounting for corrections.

The standard geometric mean deviations of the residuals in the form of minimum/average/maximum values respectively are equal 1.4/1.8/2.4 for the Ostroleka area, and 1.6/2.1/2.5 for the Warsaw Area respectively.

Thus, the data in Fig. 8 confirm the assumption made earlier in work (Vlasov et al. 2020a) that the specific activity of ¹³¹I in the atmosphere of the Ostroleka Area is greater than the data of its measurements in Warsaw city of the Warsaw Area. Thus, according to estimates made on the basis of a comparison of the minimum precipitation densities of ¹³⁷Cs in these areas, the magnitude of this excess is 2.7 times, and on average it is 2.5–3 according to Fig. 8.

From the physics of radionuclide transfer along the chain: vegetation-cattle organism-milk-human body, it follows that the maximum of activities radionuclides activities in the human body due to their consumption with milk and greens will be directly proportional to their maximum activities. Accordingly, the nutritional component of internal radiation of thyroid and the entire human body along the chain will also be directly proportional to these values. With this in mind, the discrepancy in the form of the ratio of calculated and instrumental data of the specific activities of radionuclides in milk and greens can be used to adjust the calculated data of the integral of their entry into the human body according to the following ratio:

I^cor = P_gr ∙ I^C_gr ∙ ∆⁻¹_gr + P_milk ∙ I^C_milk ∙ ∆⁻¹_milk, (7)

where

I^cor is the adjusted total integral of the entry of the activity of radionuclides with greens and milk into the human body, kBq;

P_gr and P_milk are daily consumption of greens and milk, kg/day,

I^C_gr and I^C_milk are calculated integrals of specific radionuclide activities in greens and milk, kBq/kg* day;

${\Delta }_{gr}={\left[\frac{\left(\overline{q_{gr}^{\text{dir }}}\right)}{\left.\overline{\left(q_{gr}^{\text{instr}}\right.}\right)}\right]}_{{\subset }_{\max }}$, ${\Delta }_{milk}={\left[\frac{\left(\overline{q_{milk}^{\text{dir }}}\right)}{\left.\overline{\left(q_{milk}^{\text{instr}}\right.}\right)}\right]}_{{\subset }_{\max }}$, (8)

∆_gr and ∆_milk are discrepancies of calculated q^dir and instrumental q^instr data of specific radionuclide activities in greens_gr and in milk_milk in the scope of instrumental data maximum values ⊂_max.

* – is measured in (Vlasov et al. 2023) as 0.75±1.7.

In general, it can be assumed that the calculated model prognostic properties estimated in the form of standard geometrics means values and standards deviations of the ratio of calculated instrumental milk activity data, can be estimated as 1.05±2.0. The values of these ratios for adjusting the estimates of doses of radiation to the human thyroid, as

∆_gr = 0.75 ± 1.7, ∆_milk = 1.3 ± 2.5.