where, N_Excreted was the annual N excretion for dairy cows (in kg N/yr), CP was the percentage of crude protein in diet (16%), and M was the annual milk production (in L/yr).

In order to assess gaseous N losses using the emission factors described in Table 1, the NH₄ ⁺-N content in excreta deposited in housing was 29% of total N excreted (Pereira et al., 2010) and the mineral N content in cattle slurry was 50% of total N applied at soil spreading (Trindade et al., 2009; Pereira et al., 2016). Considering Portuguese legislation (NREAP, 2013) regarding animal manure management, it was assumed a 30% reduction in NH₃ emissions at land spreading, since the untreated cattle slurry was subjected to broadcast application and incorporation by plough within 12 h (EMEP-EEA, 2013).

The CH₄ emissions from manure management of all cattle, as well as emissions from enteric fermentation of the non dairy cows, were estimated by Tier 1 approach of IPCC (IPCC, 2006) for Portuguese conditions (Table 1). For dairy cows, the CH₄ emissions from enteric fermentation were estimated by Tier 2 approach of IPCC, and in function of milk production of each farm (Table 1) as used by Casey & Holden (2005).

The relationship between milk production and gaseous emissions was established using regression analysis (e.g., fitting exponential equations). The software used was STATISTIX 7.0 (USA) and significant statistical differences correspond to p<0.05.

The main characteristics (mean±standard deviation) of the typical Portuguese dairy cattle farms studied (n=1471) were as follows: dairy cows and non-dairy cows=48±32.1 and 25±23.0 animals/farm/yr, respectively; milk production=6601±1634.5 L/cow/farm/yr; LU=67.4±48.25; total N excreted in manure=118.5±9.38 and 50±0.0 kg N/yr for dairy cows and non-dairy cows, respectively. It was observed that the cattle numbers ranged considerably between the studied farms. The number of dairy cows varied between 20 and 441 animals and milk production varied between 2000 and 13000 L/yr/cow. The non dairy cows were about 34% of total cattle housed in each farm and 42% of the 1471 commercial dairy cattle farms had an annual milk production higher than 7000 L/cow.

Table 2 shows the mean values of gaseous emissions from all stages of manure management. We observed important NH₃ emissions (>25% of total losses) at all stages of manure management, but soil application was the main source of NH₃ emissions followed by housing. A significant (p<0.05) negative relationship was observed between the intensity of milk output per cow and NH₃ emissions per litre of milk produced in each farm (Fig 1A). In our study, the NH₃ emissions were 92% of N emissions (NH₃+N₂O) of which were contributed 35, 25 and 40%, respectively, from housing, storage and soil application (Table 2). So, these values observed in each stage of manure management are comparable to values obtained in other studies, with higher NH₃ emissions in soil application followed by housing (Sommer et al., 2006). In addition, our estimates of emissions of NH₃ (expressed per litre of milk produced) are comparable with average values observed in dairy cattle farms located at Germany, Portugal and UK, with emissions that ranged between 7.5 and 7.7 g N/L milk (Fangueiro et al., 2008).

The N₂O emissions (2.6 kg N/LU/yr) from all stages of manure management were small relative to NH₃ emissions (34.7 kg N/LU/yr) observed in the farms, being less than 8% of N emissions (NH₃+N₂O) (Table 2). The main source of N₂O emissions was soil application with 75% of total losses against less than 25% in storage and housing. Considering the N₂O emissions from all stages of manure management, it was observed a significant (p<0.05) negative relationship between the increase of milk production in farms and N₂O losses per litre of milk produced (Fig 1B).

Enteric fermentation contributes with 46% of total CH₄ emissions (110 kg CH₄/LU/yr) from farms and manure management was responsible for the remaining CH₄ losses. The GHG (N₂O+CH₄) emissions, expressed in CO₂ equivalent, from the studied Portuguese dairy cattle farms were about 6.0 t/LU/yr, wherein about half of these losses are emitted from enteric fermentation and the other half coming from manure management (Table 2). In addition, the increase of milk production in farms reduces significantly (p<0.05) the CH₄ and GHG emissions per litre of milk produced in studied farms (Fig. 1C-1D).

The GHG emissions observed in the studied dairy cattle farms (1.2 kg CO₂ equivalent/L milk) (Table 2) are higher than a previous study by Castanheira et al. (2010) who reported a environmental impact (using life cycle assessment methodology) of 1.0 kg CO₂ equivalent/L milk in a typical Portuguese dairy farm (including diesel consumption). Our study does not include N₂O from mineral fertilisers, indirect N₂O emissions and CO₂ losses from direct and indirect energy use in dairy farms. Also, differences between our estimates and the previously referred study are related with an underestimate of GHG emissions coming from enteric fermentation of dairy cows reported by Castanheira et al. (2010), since they used a Tier 1 approach to estimate emissions whereas this study used a Tier 2 approach. Nevertheless, Casey & Holden (2005) calculated GHG emissions ranged from 0.9 to 1.5 kg CO₂ equivalent per litre of milk in typical Irish dairy cattle farms and found a negative relationship between GHG emissions and the intensity of milk production, being comparable with the present study. In addition, increasing milk yield/cow will reduce GHG emissions, if these emissions are expressed per kg milk and reduction in associated beef production is not considered (Zehetmeier et al., 2012).

The results obtained in our study are a logical consequence of the mathematical equations (Eq. [1]-[5]) of the methodology. Thus, Eq. [5] for N excretion and IPCC equations are very sensitive to milk yield and crude protein (for N excretion). Since emission per animal increases with production intensity, but productivity increases at a higher rate, emissions per product unit decrease and this originates the trend shown in Fig. 1. Therefore, increasing the production will reduce emissions, and improving genetics, nutrition and management will both improve productivity and reduce emissions. There were substantial differences among farms in these factors, probably related to their production objective, which explain the important differences obtained in milk production (2000-13000 L/yr) and emissions.

Previous studies (Hristov et al., 2011; Pereira & Trindade, 2014) reviewed mitigation strategies for reducing gaseous from cattle farms and are in agreement that pre-excretion techniques designed for lowering excreta (e.g., optimised crude protein in diet and increased milk production at farm level) are more efficient than post-excretion strategies (e.g., floor type and manure handling). In the present study, results obtained showed that increasing milk production in farms will reduce significantly (p<0.05) NH₃ and GHG emissions per litre of milk produced in each farm. Hence, a win-win strategy for reducing NH₃ and GHG emissions from dairy cattle farms will be the increase of milk production in these farms. For example, a farm with 10000 L/cow of annual milk production should had an amount 25% lower of NH₃ and GHG emissions, expressed per litre of milk produced, relative to a farm with a annual milk production of 6600 L/cow. A high milk production per cow will result in fewer cows to achieve the same level of production relative to less intensive dairy farm. On the other hand, the reduction of replacement animals (heifers) has a similar effect than high milk production per cow and could reduce NH₃ and GHG emissions in farms.

In conclusion, the manure management and enteric fermentation in a typical Portuguese cattle farm contributes with 7.5±0.15 g N/L milk produced as NH₃ and 1.2±0.22 kg CO₂ equivalent per litre of milk as GHG. Besides, increasing milk production in farms will reduce significantly NH₃ and GHG emissions per litre of milk produced in each farm. It can be concluded that a win-win strategy for reducing NH₃ and GHG emissions from dairy cattle farms will be the increase of milk production on these farms. This goal can be achieved by implementing animal breeding programs and improving feed efficiency in order to increase productivity.