#### 3.1. Drinking Water Demand

The daily drinking water intake per cow throughout the observation period is shown in

Figure 2. The drinking water demand of the cows in the AMS showed a seasonal response, being highest in the summer and lowest in the winter. This corresponds with the changes of the daily mean air temperature during the year (

Figure 3). Cardot et al. [

7], Holter and Urban [

8], Meyer et al. [

9] and Murphy et al. [

10] also identified the drinking water intake as dependent on the temperature or season. The drinking water intake of the cows in the HBP did not show such a seasonal response. Since the group of cows in the HBP was more heterogeneous than in the AMS, the effects of temperature on drinking water intake may have been leveled out.

The drinking water intake changed not only over the year, but also during the day (

Figure 4). Between 05:00 and 21:00 h the cows drink 80% of their daily water intake. During this time the workers were in the barn and it was lit. The peak of drinking water intake was observed between 07:00 and 08:00 h for the cows in the AMS, and between 07:00 and 08:00 h and between 17:00 and 18:00 h for the cows in the HBP. This was expected, since the cows in the HBP were milked at these times, and cows drink large amounts of water after milking [

7].

The milk yields were needed to calculate the drinking water demand per kg milk and to assess the accuracy of the available regression functions for estimating the drinking water demand of dairy cows. Milk yields are shown in

Figure 5 and

Table 1. The average milk yield of the 88 cows milked in the AMS was 35.5 kg milk per cow per day, with an average of 2.8 milkings per day and 12.7 kg milk per milking. On average, 92 cows were milked twice per day in the HBP, with an average milk yield of 25.4 kg milk per cow per day or 12.7 kg per milking.

Figure 5 is more detailed for the AMS, as milk yield data was available for each milking in contrast to the data for milk yield in the HBP.

The 88 cows in the AMS group drink on average 8.0 m

^{3} of water per day. This is equivalent to 91.1 L water per cow per day, or 2.6 L per kg milk. Holter and Urban [

8] suggested a rule of thumb of 2 L drinking water per kg milk, which is 77% lower than the measured value. The diet provided 34.8 L water, which represented 27% of the total water intake. The calculation of the drinking water demand according to Meyer et al. [

9] leads to an underestimation of the drinking water demand by 6.9 L per day, and according to Holter and Urban [

8] to an underestimation by 14.8 L per day, while using the regression function of Cardot et al. [

7] the drinking water demand was overestimated by 4.6 L per day. The difference between the measured minimum and maximum water intake is 67.7 L per day, while the range of estimated values includes 26 L [

7], 13 L [

8], 62 L [

9] and 44 L [

10].

The 92 cows in the HBP group drank on average 5.0 m

^{3} of water per day, representing a mean drinking water demand of 54.4 L water per cow per day or 2.1 L per kg milk. This was 10% more than Holter and Urban’s [

8] rule of thumb. The diet provided 32 L water, which was 36% of the total water intake.

The measured drinking water demand of the cows in the AMS and the HBP, the

milk yield of the cows (kg·cow

^{−1}·day

^{−1}) and the

mean temperature (°C) were used to develop a new regression function for the modeling of the daily drinking water demand of cows in the barn (

W_{drink-cow_daily}):

A comparison of the measured and modeled daily drinking water demand is provided in

Table 2. It was found that the function developed in this study was closest to the perfect slope of 1, while the function of Meyer et al. [

9] had the smallest

y-intercept. A slope of 1 and a

y-intercept of 0, using standard regression, indicate that the model perfectly fits the measured data [

23]. The coefficient of determination (

R^{2}) shows the proportion of the variance in the measured data that is explained by the model, with values closer to 1 indicating less error variance. The regression functions had

R^{2} values ranging from 0.45 [

7] to 0.69 [

8], indicating that the regression functions did not include all of the parameters that affect the water intake of the cows. However, since values >0.5 are generally considered acceptable [

24,

25], all of these models were more or less acceptable. All of the previously published regression functions were based on investigations that were conducted from early to mid-lactation [

7,

8,

9,

10], and so did not cover the period of lactation when the milk yield—and hence the drinking water demand—is lower. By contrast, in the present study, the cows milked in the HBP were at the end of lactation. Therefore, this may explain why the calculated drinking water demand from all regression functions, except that of Holter and Urban [

8], was significantly higher than our measured values from the HBP.

Only the function developed in this study showed acceptable NSE and NSElog values of >0.5, although the function of Holter and Urban [

8] also resulted in an acceptable value of >0 for NESlog; the peaks resulting from a larger drinking water demand affected this model’s performance. In general, model simulation with dimensionless model evaluation statistics can be considered satisfactory if NSE > 0.50 and RSR < 0.70, and if PBIAS < 25% for streamflow [

20]. By contrast, an NSE value < 0.0 shows that the mean observed value is a better predictor than the simulated value, indicating unacceptable performance. The logarithmic transformed NSE (NSElog) lowers the tendency of the NSE to overvalue large peaks.

The function developed in this study also showed the lowest RMSE, RSR, and BIAS error indices. RSR values of 0 indicate a perfect fit using the absolute error index statistic, and so the RSR values for the other functions (>0.70) must be considered unsatisfactory. Residual variance is the difference between the measured and simulated values, and is often estimated by the residual mean square or root mean square error (RMSE). The lower the RSR, the lower the RMSE, which indicates a better model simulation performance. The BIAS was larger for the previously published functions, which measures the average tendency of the simulated constituent values to be larger or smaller than the measured data.

In the literature studies of Cardot et al. [

7], Holter and Urban [

8], Meyer et al. [

9], and Murphy et al. [

10], more parameters influencing water intake were investigated than were finally included in the new regression function. It cannot be ruled out that these parameters could have a greater influence on the water intake of the cows in this study. Using the regression function of the earliest study predicted the water intake best, although the genetics, physiology, and milk yield of the cows has changed over the years. Further reasons for the difference between estimated and measured drinking water intake may be factors that were not investigated, such as rank fights, sexual cycle, and disturbance caused by external factors.

Our regression function includes only two parameters, since others such as live weight, dry matter intake, or sodium intake were not measured in this commercial dairy herd. The coefficients of the parameters in this function are not comparable with other studies, since every study includes its own parameters in the regression functions. The coefficient and hence the influence of the milk yield on drinking water intake in this study is comparable to the other regression functions. This can be explained by the interdependence of the different parameters, for example a higher dry matter intake will lead to a higher milk yield. If the dry matter intake is not included in the regression function, a part of its influence will be compensated by the milk yield parameter [

26]. The

R^{2} of our regression function is 0.67, which lies between the

R^{2} of Cardot et al. [

7] at 0.74 and that of Murphy [

10] at 0.59.

#### 3.2. Cleaning Water Demand

The daily cleaning water demand of the HBP and the AMS is shown in

Figure 6. Neither milking system showed a seasonal pattern for cleaning water demand. The cleaning water demand was higher in the HBP than in the AMS. The daily cleaning water demand ranged from 1.1 m

^{3} to 18.1 m

^{3} in the AMS and from 1.1 m

^{3} to 15.2 m

^{3} in the HBP.

For cleaning the AMS, on average 2.5 m

^{3} water was used per day (

Table 3). Per cow per day, 28.6 L water was needed. Related to the milk yield of the cows, 0.8 L water was used per kg milk to clean the AMS. The cleaning of the milk tank required 0.2 m

^{3} water per day or 7% of the total water use in the AMS.

For cleaning the HBP, 3.1 m

^{3} water was used per day (

Figure 6,

Table 3). Per cow per day 33.8 L water was used, which is 5.2 L per day or 18% more than in the AMS. For cleaning the surface of the milking parlour 2.0 m

^{3} water was used. Fourteen litres of cleaning water per square metre was used in the HBP. Cleaning of the milking system required 0.7 m

^{3} water per day and cleaning of the udder prior to milking 0.3 m

^{3} per day. 0.1 m

^{3} water per day was used for cleaning the milk tank, which is 4% of the total technical water use. Related to the milk yield, 1.3 L per kg milk was used for cleaning.

Leaks amount to 1% of the measured technical water use in the barn and were mainly caused by disrupted hoses. Hose disruption seldom occurred (5 times during the observation period), but can result in high water loss if this happens at night and is only detected hours later in the morning when the first workers enter the barn.

The high cleaning water use in the HBP was caused by the cleaning system and the fact that there was no incentive to save water. The cleaning was performed with a high-pressure cleaner and a hose with a large diameter. The water was supplied via the farm’s own bore, so that no costs were incurred for the water, only energy costs for pumping. Furthermore, the water was deliberately added to the slurry to keep it pumpable. This leads to high water demand for cleaning the surface of the parlour.

In the studies by Jensen [

12] and Rasmussen and Pedersen [

14], the cleaning water use was 0.2–0.4 L water per kg milk, which is less than half of what we measured. In their studies the AMS were optimized for low water use and were operated with the maximum number of cows. The higher water demand by the commercial farm in our study was also explained by withdrawal of water which was not directly used to clean the AMS, but to clean the barn of the cows in the AMS. Chapagain and Hoekstra [

27] estimated the cleaning water demand in their calculation of the virtual water at 22 L per cow per day, which is 6.6 L less than measured in the AMS and 11.8 L less than in the HBP. A cleaning water demand of 0.3 L water per kg milk was estimated in a life cycle assessment study by Eide [

28] for Norwegian conditions, which is 60% less than in this study. KTBL [

13] estimated 2 L per square meter for cleaning an HBP, which is one seventh of what we measured.

In the AMS the share of drinking water demand was 76% and the share of cleaning water 24% of the total technical water demand. This is comparable with the results of Drastig et al. [

1]. In the HBP, 62% of the water was needed for drinking and 38% for cleaning. The difference is explained by the higher cleaning water demand per cow and the lower drinking water demand per cow in the HBP. It is difficult to make general statements about reductions of the water demand in a dairy barn, since regression functions of the water demand only cover up to two thirds of the influencing parameters. The variation in cleaning water demand between the milking systems was less than the water demand for cleaning the surface of the parlours. Cleaning of the milking system was computer-controlled, while the surface of the parlour was cleaned by hand. The soiling depends on the cows. The water demand can be reduced by educating the workers to reduce water use, by using high-pressure cleaners or mechanical cleaning methods such as a brush. The cleaning water demand per liter of milk could be reduced with more milk milked per cleaning cycle, if the total cleaning water demand cannot be reduced. This could be achieved with more cows, if the barn allows, or higher milk yields of the cows. The findings of this study with respect to the cleaning water demand are only applicable to this particular barn with its milking and cleaning systems. Therefore, further detailed measurements in other barns are required to make general statements about methods for reducing the cleaning water demand.