V M Thorup
email: vivim.thorup@agrsci.dk

D Edwards

N C Friggens

On-farm estimation of energy balance in dairy cows using only frequent body weight measurements and body condition score

Keywords: energy balance, body condition score, body weight, modeling

Precise energy balance estimates for individual cows are of great importance to monitor health, reproduction, and feed management. Energy balance is usually calculated as energy input minus output (EB inout ), requiring measurements of feed intake and energy output sources (milk, maintenance, activity, growth, and pregnancy). Except for milk yield, direct measurements of the other sources are difficult to obtain in practice, and estimates contain considerable error sources, limiting on-farm use. Alternatively, energy balance can be estimated from body reserve changes (EB body ) using body weight (BW) and body condition score (BCS). Automated weighing systems exist and new technology performing semi-automated body condition scoring has emerged, so frequent automated BW and BCS measurements are feasible. We present a method to derive individual EB body estimates from frequently measured BW and BCS and evaluate the performance of the estimated EB body against the traditional EB inout method. From 76 Danish Holstein and Jersey cows, parity 1 or 2+, on a glycerol-rich or a whole grain-rich total mixed ration, BW was measured automatically at each milking. The BW was corrected for the weight of milk produced and for gutfill. Changes in BW and BCS were used to calculate changes in body protein, body lipid, and EB body during the first 150 d in milk. The EB body was compared with the traditional EB inout by isolating the term within EB inout associated with most uncertainty; that is, feed energy content (FEC); FEC = (EB body + EMilk + EMaintenance + Eactivity)/dry matter intake, where the energy requirements are for milk produced (EMilk), maintenance (EMaintenance), and activity (EActivity). Estimated FEC agreed well with FEC values derived from tables (the mean estimate was 0.21 MJ of effective energy/kg of dry matter or 2.2% higher than the mean table value). Further, the FEC profile did not suggest systematic bias in EB body with stage of lactation. The EB body estimated from daily BW, adjusted for milk and meal-related gutfill and combined with frequent BCS, can provide a successful tool. This offers a pragmatic solution to on-farm calculation of energy balance with the perspective of improved precision under commercial conditions.

INTRODUCTION

The notion that early lactation is associated with decreased health and reproduction is widely accepted [START_REF] Ingvartsen | On the relationship between lactational performance and health: Is it yield or metabolic imbalance that cause production diseases in dairy cattle? A position paper[END_REF]. Increased levels of digestive and locomotion disorders in early lactation and delayed reproduction have been linked with more lengthy and severe periods of negative energy balance; that is, greater body reserve mobilization [START_REF] Frigo | The genetic relationship of body weight and early-lactation health disorders in two experimental herds[END_REF]. Therefore, estimates of the dairy cow's energy balance are of great importance to monitor health, reproduction, and feed management. Traditionally, energy balance in dairy cows has been calculated as energy input minus energy output (EB inout ;Friggens et al., 2007a;[START_REF] Banos | Genetic association between body energy measured throughout lactation and fertility in dairy cattle[END_REF]. The EB inout method requires that feed energy intake and energy expenditure (milk, maintenance, activity, growth, and pregnancy) are recorded, and with the exception of milk yield, direct measurements of these sources are difficult to obtain in practice. Further, these calculations contain considerable error (Ellis et al., 2006a,b). An alternative is to estimate energy balance from changes in body reserves (EB body ), which involves measurements of BW and BCS [START_REF] Coffey | Genetic evaluation of dairy bulls for energy balance traits using random regression[END_REF][START_REF] Tedeschi | Accounting for energy and protein reserve changes in predicting diet-allowable milk production in cattle[END_REF]Friggens et al., 2007b). Although measuring BW and BCS is feasible in practice, until recently the method was not very suitable for detecting short-term changes because of infrequent BW and BCS measurements. Infrequent measurements make it difficult to detect and reduce noise in the time series of measurements. Automated weighing systems (often in the milking parlor) have become commercially available, and new technology within the field of semi-automated body condition scoring has emerged [START_REF] Halachmi | Cow body shape and automation of condition scoring[END_REF][START_REF] Bewley | Potential of Using New Technology for Estimating Body Condition Scores[END_REF][START_REF] Azzaro | Objective estimation of body condition score by modeling cow body shape from digital images[END_REF]. Consequently, fully automated, frequent BW and BCS measurements now seem within reach. For the dairy farmer, the ability to assess the energy balance for individual cows on-farm would be a very attractive management tool. Estimating EB body from daily, noise-reduced BW measurements that are adjusted for milk and meal-related gutfill and that are combined with frequent BCS measurements could provide such a tool. This would be a pragmatic solution to on-farm calculation of the energy balance of individual cows that offers the perspective of a significant improvement in the precision of energy balance estimation.

The purposes were to (1) present a method for deriving EB body estimates for individual cows from frequently measured BW and BCS, and (2) evaluate the performance of our EB body method against the traditional EB inout method.

MATERIALS AND METHODS

Cows and Experimental Procedures

The data consisted of longitudinal measures of 76 cows through the first 150 DIM that allowed calculation of both EB body and EB inout . The 76 cows were primiparous (n = 51) or multiparous (n = 25, lactations 2 to 4) cows, calving from January to May 2008. Further, 57 cows were Danish Holsteins (DH) and 19 cows were Jerseys. All cows were loose-housed in a barn at the Danish Cattle Research Center (Tjele, Denmark) with an automatic milking system (VMS, Voluntary Milking System, DeLaval, Tumba, Sweden) and automatic feeding stations (Roughage Intake System, Insentec BV, Marknesse, the Netherlands). The data came from cows that were in a feeding experiment and had ad libitum access to 1 of 2 TMR: 44 cows were on a glycerol-rich diet (TMR 1: 15% of DM was glycerol, 7% was wheat bran and soybean meal), and 32 were on a whole grain-rich diet (TMR 2: 22% of DM was whole grain NaOH-treated wheat). The average performances of milk yield (MY), milk fat, milk protein, DMI, and smoothed BW of the cows grouped by breed and diet are in Table 1.

At each milking the cows were weighed automatically on a weighing platform (Bjerringbro Vaegte, Bjerringbro, Denmark) installed in the VMS. Milk yield was recorded at each milking, and composite milk samples from all milkings in a 48-h period were taken and analyzed for fat, protein, and lactose content once weekly. The BCS was assessed every 2 wk by trained observers to the nearest quarter unit on a scale from 1 (emaciated) to 5 (obese; [START_REF] Ferguson | Principal descriptors of body condition score in Holstein cows[END_REF].

All procedures involving animals were approved by the Danish Animal Experiments Inspectorate and complied with the Danish Ministry of Justice Law no. 382 (June 10, 1987) and Acts 739 (December 6, 1988) and 333 (May 19, 1990) concerning animal experimentation and care of experimental animals.

Milk-Free and Meal-Related Gutfill-Free BW

While the cow was standing on the weighing platform in the VMS, her BW was automatically recorded 6 times/s during the milking. For each VMS milking, the end-weight, or so-called milk-free BW (BW mf ), was derived from the weighing platform data as follows. First, cleaning rules were applied to exclude artifacts. If the median BW during the milking was <200 kg, or if >30% of the values were under a threshold of the median BW minus 75 kg, all data obtained during that particular milking were excluded. Initial and final time intervals (i.e., when the cow was only partly on the weighing platform as she entered or left the VMS) were defined as intervals for which >50% of the values were under the threshold; these were excluded from the data set for that particular cow. To obtain a simple and robust estimate of BW mf , the remaining values were cubic spline-smoothed using 3 knots, and BW mf was defined as the final value in the remaining interval. This is illustrated in Figure 1.

An example of BW mf relative to DIM is shown in Figure 2. The noise in this time-series is mainly due to variation in gutfill associated with the temporal pat- tern of meals ingested by the cow (in systems with VMS there is no fixed relation between time of milking and times of feed distribution). Consequently, a meal-related gutfill-free BW (BW gff ) was derived from the BW mf for the first 150 DIM using the following logic. Gutfill (GF) can be considered as the sum of 2 components: a large meal-related component that is a function of the feed intake pattern in the preceding hours, and a smaller residual component remaining in the gut that is assumed constant on this time-scale.

To eliminate the meal-related gutfill variation, BW gff was derived from BW mf by quantile regression [START_REF] Koenker | Quantile regression[END_REF] using the 20% lower quantile of the distribution in a cubic spline function with nonequidistant knots, an example of which is in Figure 2. The lower 20% quantile was chosen because this is close to the proportion of residual GF to total GF found for normal diets (Martin and Sauvant, 2010b) and because, empirically, this provides a suitable offset where the fit is not perturbed by extreme outliers. In this process, if 2 consecutive BW mf differed by more than 200 kg, then the lower weight was excluded. Using equidistant knots did not model the weight decline in early lactation well, therefore nonequidistant knots at 1, 12, 20, 60, 115, and 150 DIM were chosen, in accordance with Friggens and colleagues (2007a).

The BCS data were smoothed across lactation using natural cubic splines of degree 3 [START_REF] Hastie | Generalized Additive Models[END_REF]). An example of BCS observations and smoothed BCS curve for 1 cow relative to DIM is in Figure 3.

Calculation of EB body

Because any discrepancy between energy inputs and outputs must be met by changes in body energy, EB body (MJ/d) can be calculated from changes in body lipid (BL) and body protein (BP): EB body = z × ΔBL + y × ΔBP, [1] where ΔBL is the rate of change in BL (kg/d); ΔBP is the rate of change in BP (kg/d); z is the energy associated with BL change (MJ/kg); and y is the energy associated with BP change (MJ/kg).

It has been shown that BL (kg) can be estimated from BCS [START_REF] Wright | Estimation in vivo of the chemical composition of the bodies of mature cows[END_REF]:

BL = EBW × (a + b × BCS), [2]
where EBW is empty BW, and a (kg of lipid/kg of EBW) and b (kg of lipid/kg of EBW/unit of BCS) are constants relating BCS to body fatness. Thus, the rate of change in BL can be estimated from the change in EBW (ΔEBW) and the change in EBW × BCS [Δ(EBW × BCS)] as

ΔBL = a × ΔEBW + b × Δ(EBW × BCS); [3] BP (kg) is assumed a constant proportion, k, of lipid- free EBW (LFEBW, kg): BP = k × LFEBW, [4]
Given that the sum of LFEBW and BL is EBW, and then substituting equation [3] for ΔBL:

ΔBP = k × (ΔEBW -ΔBL), ΔBP = k × [(1 -a) × ΔEBW -b × Δ(EBW × BCS)].
[5]

Substituting equations [3] and [5] in equation [1] gives

EB body (MJ/d) = z × [a × ΔEBW + b × Δ(EBW × BCS)] + y × k × [(1 -a) × ΔEBW -b × Δ(EBW × BCS)]. [6]
The constants k (0.2224 kg/kg), y (13.5 MJ/kg of mobilized and 50.0 MJ/kg of deposited protein), and z (39.6 MJ/kg of mobilized and 56.0 MJ/kg of deposited lipid) can be regarded as generic, and the energy units used are effective energy (EE; [START_REF] Emmans | Effective energy: A concept of energy utilization applied across species[END_REF]. In this system, 1 MJ of EE supply has the same energy value as 1 MJ of lipid loss from the body. Thus, the EE values assigned to feeds are directly equivalent to the energy requirements of the animal. Because the constants y and z depend on whether protein and fat are being mobilized or deposited, the lactation period was partitioned for simplicity into 3 periods. We assumed that during the first period (early lactation: d 0 to 28), lipid and protein are both mobilized [START_REF] Cammell | An examination of energy utilisation in lactating dairy cows receiving a total mixed ration based on maize silage[END_REF]; during the second period (peak lactation: d 29 to 70), lipid is mobilized and protein may be deposited; and finally during the third period (mid lactation: d 71 to 150), both lipid and protein are being deposited. The constants a and b were assumed to have the values 0.05 kg of lipid/kg of EBW and 0.10 kg of lipid/kg of EBW/ unit of BCS; details of estimation are given by Friggens et al. (2007b).

Derivation of EBW from BW

The difference between BW and EBW is assumed to be primarily due to fill of the gut, udder, and uterus. Udder fill is accounted for by the derivation BW mf , uterine fill we assume negligible, because this study focuses on the first 150 DIM, and this leaves GF to be adjusted for. The adjustment for GF is greatly facilitated by having accounted for meal-related variation in gutfill (BW gff , described above), so this leaves residual gutfill to be corrected for, which is described below. Martin and Sauvant (2010b) showed that, across a wide range of feeding conditions, the daily trend in decay in residual gutfill (dRGF/dt) can be described as follows:

dRGF/dt = FMI -f × (GF -δ × LFEBW), [7].
where RGF is residual gutfill (kg), FMI is daily fresh matter intake (kg/d), f is the fractional daily rate of removal of digestive contents, GF is the meal-related GF (kg), and δ is the RGF as a proportion of LFEBW (kg/kg).

Equation [7] contains intake, which is inconvenient because this study aimed to derive an energy balance measure that did not require measurement of intake. Using an approximation that has trivial consequences on the calculations permits the removal of intake from the calculation. In the situation where meal-related GF has been removed and daily intake is stable, by definition, GF is constant and thus dRGF/dt is 0, so

FMI = f × (RGF -δ × LFEBW), RGF/LFEBW = FMI/(f × LFEBW) + δ.
[8]

This shows that, at a given stable level of intake, RGF is a constant proportion of LFEBW. Further, simulation across a wide range of FMI (9 to 54 kg/d) showed that the variation in the value of RGF/LFEBW has a very small effect on estimation of EBW. For example, when estimates of EBW using a constant value of RGF/LFEBW of 0.26 are compared with estimates of EBW throughout lactation calculated using a lacta-tion curve of FMI increasing from 25 to 55 kg/d at peak before tailing off to 20 kg/d [START_REF] Friggens | Feed intake relative to stage of lactation for dairy cows consuming total mixed diets with a high or low ratio of concentrate to forage[END_REF], the maximum discrepancy was just 3% in EBW. Thus, we believe it is an acceptable approximation to assume that RGF/LFEBW (kg/kg), hereafter called g, is constant, and assumed 0.26. Given g, EBW can be calculated as EBW = BW gff -g × LFEBW = BW gff -g × (EBW -BL).

[9]

Substituting equation [2] in equation [9]:

EBW = BW gff -g × {EBW -[EBW × (a + b × BCS)]} = BW gff /[1 + g × (1 -a -b × BCS)]. [10]

Model Evaluation

Testing a traditional EB inout calculation is usually done by comparing the weight change to the end of the lactation with the cumulated EB inout . This approach was not feasible with EB body , as this would imply having BW on both sides of the equation, making it a circular test. If EB inout could be assumed error-and bias-free, then it would be logical to compare EB body to EB inout directly. It has been shown that this assumption does not hold (Ellis et al., 2006a,b). To deal with this, the uncertainty in EB inout was isolated on one side of the equation and this value was estimated, namely the feed energy content (FEC). When feed composition is not altered, and ignoring possible intake effects on digestibility (FEC is largely unaffected by level of feeding when expressed in EE units; [START_REF] Emmans | Effective energy: A concept of energy utilization applied across species[END_REF], the true FEC value is not expected to change with DIM. Thus, to evaluate the EB body method, systematic trends in FEC were calculated from EB body and EB inout components, relative to DIM. The manipulation to derive calculated FEC was as follows:

EB inout = EIntake -(EMilk + EMaintenance + EActivity),
where EIntake is feed energy intake, EMilk is energy required for MY, EMaintenance is energy required for maintenance, and EActivity is energy required for activity. And, assuming that EB inout = EB body , then EB body + EMilk + EMaintenance + EActivity = EIntake.

Because EIntake = FEC × DMI, then FEC (MJ of EE/kg of DMI) = (EB body + EMilk + EMaintenance + EActivity)/DMI, [11] where EB body is calculated according to equation [1], and EMilk, EMaintenance, and EActivity are defined below using the EE system [START_REF] Emmans | Effective energy: A concept of energy utilization applied across species[END_REF]. The above test to compare EB body and EB inout , using equation [11], would be valid using other energy systems, provided that there was equivalence between supply and expenditure energy units:

EMilk (MJ of EE/d) = EFat + EProtein + ELactose, [ 12
]
where EFat = MY × (milk fat percentage/100) × 56, and is the energy required to produce 1 kg of milk fat (MJ of EE/kg); EProtein = MY × (milk protein percentage/100) × 33, and is the energy required to produce 1 kg of milk protein (MJ of EE/kg); and ELactose = MY × (milk lactose percentage/100) × 18, and is the energy required to produce 1 kg of milk lactose (MJ of EE/kg). These energy values are in accordance with [START_REF] Emmans | Consequences of genetic change in farm animals on food intake and feeding behaviour[END_REF].

EMaintenance (MJ EE/d) =

1.63 × (BP/BPmat 0.27 ), [13] where BPmat is body protein at maturity. For parity 3 and older cows, BPmat was assumed 0.2224 (kg/kg) × LFEBW (kg; calculated from EBW standardized to BCS 3) at 112 DIM. Parity 2 cows were assumed 94% of mature size, and parity 1 cows 85% of mature size, at the same DIM (Friggens et al., 2007a).

EActivity (MJ of EE/d) = 0.01 × BW gff . [14]
The calculations of EIntake, EMilk, EMaintenance, and EActivity have been described in detail by Friggens et al. (2007a). For calculating EB inout in the present study, no smoothing was applied to the base observations of DMI, MY, or milk composition for the purpose of deriving EMilk, EMaintenance, EActivity, and FEC.

Statistical Analysis

All data manipulation was performed using the R software (R Development Core Team, 2011). Before calculating EB body averages, observations of EBW changes exceeding more than -7.5 or +5 kg/d were excluded (affecting 87 out of 10,497 observations).

The FEC was calculated only for days on which information on DMI, MY, and milk components was available; this data set contained 1,108 observations. The FEC was tested using PROC MIXED in SAS with the Kenward-Roger degree-of-freedom procedure due to unbalanced data because of missing observations [START_REF] Littel | SAS for Linear Models[END_REF]. A full model initially included breed, parity, diet, DIM, and the 2-way interactions. One cow was excluded from analysis; otherwise, the model would not converge:

FEC ijklm = μ + breed i + parity j + diet k + cDIM m + (cDIM m × breed i ) + (cDIM m × parity j ) + (cDIM m × diet k ) + cow l + ε ijklm ,
where breed (i = DH, Jersey), parity (j = 1, 2+), and diet (k = TMR 1, TMR 2) were fixed effects, and cDIM was a continuous time variable (m = -75, …, 75) centered on DIM = 75 to minimize correlations between slope and intercept parameters, cow (l = 1, …, 75) was included as a random effect, and ε ijklm was the random residual error term associated with the ijklmth observation. To take into account the correlation from the same cow, ε ijklm was assumed to follow a multivariate normal distribution for each cow with a Toeplitz covariance structure [START_REF] Littel | SAS for Linear Models[END_REF]. Stepwise removal of nonsignificant effects reduced the model to the following (the main effect of cDIM was excluded to allow direct testing, on each diet, for slopes different from zero):

FEC iklm = μ + breed i + (cDIM m × diet k ) + cow l + ε iklm .

RESULTS

Examples of EB body trajectories relative to DIM for 4 individual cows are illustrated in Figure 4. The small disruptions at 28 and 70 DIM are caused by the assumed transition points of BL and BP between mobilization and deposition.

The average EB body trajectories relative to DIM for cows grouped by breed, parity, and diet and the standard deviation are in Figure 5. Visual inspection suggested that in early lactation, DH cows had a greater negative energy balance than Jersey cows, but recovered more quickly such that Jerseys appeared to have a lower EB body than DH from 30 DIM onward (Figure 5A). In early lactation, multiparous cows seemed to be in more negative EB body than primiparous cows, but no consistent differences were observed between parities later in lactation (Figure 5B). With respect to diet, cows on TMR 1 appeared to start in a more negative EB body than TMR 2, but from 50 DIM on, no consistent differences were observed between diets (Figure 5C). The standard deviation of EB body relative to DIM is in Figure 5D, providing a measure of the variation between individuals.

We evaluated EB body relative to Emilk output and DMI in the form of estimated FEC. Parity had no significant effect on FEC. Regarding breed, Jerseys had a significantly higher FEC (9.74 ± 0.10 MJ of EE/kg of DM) than DH cows (9.18 ± 0.11 MJ of EE/kg of DM; t-value = -5.09, P < 0.0001). Here, it is noteworthy that Jerseys had a 2.45 kg (corresponding to 13%) lower DMI than DH cows (Table 1). A significant diet by DIM interaction was observed for FEC. As shown in Figure 6, for TMR 2, a highly significant effect (tvalue = -3.86, P < 0.0001) was found for DIM, which decreased FEC by 0.007 MJ of EE/kg of DM per day. For TMR 1, the effect of DIM on FEC was significant (t-value = -2.00, P = 0.05), decreasing FEC by 0.003 MJ of EE/kg of DM per day. The FEC calculated from feed composition and table values were similar for the 2 diets: 9.2 MJ of EE/kg of DM for TMR 1 and 9.3 MJ of EE/kg of DM for TMR 2, which agreed well with the average 9.46 MJ of EE/kg of DM estimated from our analysis. The random animal effect on FEC accounted for 12.8% of the total variability in the data.

DISCUSSION

The EB body curves relative to DIM for the different breeds (Figure 5A) and parities (Figure 5B) compare well with other studies [START_REF] Oldenbroek | The performance of Jersey cows and cows of larger dairy breeds on two complete diets with different roughage contents[END_REF]Friggens et al., 2007a;[START_REF] Banos | Genetic association between body energy measured throughout lactation and fertility in dairy cattle[END_REF]. Diet-related differences in energy balance (Figure 5C) have been reported [START_REF] Van Knegsel | Dietary energy source in dairy cows in early lactation: Energy partitioning and milk composition[END_REF]. In evaluating the energy balance calculated from frequently measured BW measurements and BCS, we chose not to regress EB body on EB inout because such a regression would imply that EB inout is closer to the true energy balance. Although EB inout (NRC, 2001) was considered the gold standard in estimating EB, Ellis et al. (2006a) challenged the notion of EB inout actually being the gold standard (when not using calorimetry) by showing that with this traditional EB model, predicted BW differed significantly from observed values, and BW tended to be increasingly overpredicted with progressing lactation. Because of these findings, an alternative approach was chosen for evaluating EB body , a "proof by induction" approach. This approach recognizes that the main uncertainty in calculating EB inout relates to the estimation of FEC, which is usually derived from tabulated values based on feed ingredient composition and assumed digestibilities. Small errors in the assumed FEC value rapidly accumulate to produce the type of error identified by Ellis et al. (2006a). We chose to rearrange the equation linking EB body and EB inout to isolate the FEC term; that is, estimate FEC from EB body plus energy outputs in milk and maintenance (as detailed in the Materials and Methods section). Thus, estimates of FEC were obtained relative to DIM (Figure 6). Feed composition did not change, so a simple hypothesis for evaluating the EB body method is that DIM should have no significant effect on FEC. This hypothesis assumes that there are no correlated changes in TMR ingredient composition (e.g., changes in silage composition as the collection progresses through the silage bunker), that changes in FEC due to variability in DMI were negligible (Emmans 1994), and that the accuracy of measurement of TMR intake (e.g., changes in proportion of feed spilled by the cows) did not change. A secondary hypothesis would be that parity should have no effect on FEC, and breed should have little or no effect on FEC. Breed effects could be envisaged due to factors such as between-breed differences in distribution of body fat between subcutaneous and internal fat depots affecting the coefficients relating BCS to body fatness, although such effects are likely to be small [START_REF] Wright | Estimation in vivo of the chemical composition of the bodies of mature cows[END_REF]Friggens et al., 2007b).

Breed had a small effect and parity had no significant effect on FEC. This is an important result because substantial differences existed in BW and performance between the breeds represented in this study (Table 1). Therefore, this finding indicates that the EB body method is robust to large differences in size and performance. The finding that the estimated FEC was higher for Jersey cows would agree with the finding that Jerseys have greater digestive efficiency and lower intakes compared with larger breeds [START_REF] Ingvartsen | Jersey cows have a higher feed intake capacity and higher rate of passage than Friesian cows[END_REF], or it could be due to inherent breed differences in fat depots. With regard to the effect of DIM on FEC estimates, FEC showed a significant decline relative to DIM, especially on TMR 2 (Figure 6). Such a decline could be explained by deterioration in forage digestibility with time, or a progressive increase in feed wastage as a proportion of intake. Alternatively, it could be a bias in the EB body method; for example, if systematic changes occurred in RGF with DIM, although simulation of changes in RGF had only a very minor effect on estimation of EBW, and this would not explain the difference between TMR in this effect. Another possi-bility, raised by Ellis et al. (2006b), is that bias related to stage of lactation exists in estimation of maintenance energy requirements. Regardless of the cause, this DIM effect on FEC accounted for only a very small proportion (5.3%) of the total variability in the data. Further, the average estimated FEC value (9.46 MJ of EE/kg of DM) was very similar to the table values for both diets (9.2 and 9.3 MJ of EE/kg of DM), which is well within the range of error of estimating FEC from feed table estimates of digestibility (Ellis et al., 2006a). Thus, using this "test by induction," the results suggest that the present method for calculating energy balance from frequently measured BW measurements and BCS (EB body ) is an adequate method for measuring energy balance on farm without having to measure DMI or MY. Interestingly, the use of BW and BCS for improving predictions of, for example, breeding values for body energy usage or intake requirements, is becoming increasingly accepted [START_REF] Tedeschi | Accounting for energy and protein reserve changes in predicting diet-allowable milk production in cattle[END_REF][START_REF] Banos | Genetic association between body energy measured throughout lactation and fertility in dairy cattle[END_REF]. [START_REF] Tedeschi | Accounting for energy and protein reserve changes in predicting diet-allowable milk production in cattle[END_REF] used 2 models (a model based on NRC and a model based on published data on BW and BCS changes) and 2 adjustment methods (1 method using first and last BCS values and 1 method using mean of weekly BCS values). They showed that adjusting ME-and MP-allowable milk production for changes in BCS improved the precision and accuracy of both models.

An alternative to using automated BCS is to simplify the model by assuming that BP change is zero, or assume a standard ΔBP. In mature cows after early lactation, it is reasonable to assume that ΔBP is zero [START_REF] Cammell | An examination of energy utilisation in lactating dairy cows receiving a total mixed ration based on maize silage[END_REF][START_REF] Van Knegsel | Dietary energy source in dairy cows in early lactation: Energy partitioning and milk composition[END_REF]. In this case, equation [1] reduces to EB body = z × ΔBL + y × 0, and equation [5] reduces to 0 = k × (ΔEBW -ΔBL), and further to ΔBL = ΔEBW. Therefore, when BP change is zero, EB body can be estimated using only BW measurements because in this situation EB body = z × ΔEBW.

Although the EB body method presented has the potential to provide on-farm energy balance measures, the present study should be regarded as a proof-of-concept rather than a definitive method. Several issues remain to be further explored. In particular, the smoothing method used for deriving the meal-related gutfill-free BW is not suitable for real-time usage. As on-farm applications already exist that employ real-time smoothing techniques [START_REF] Nielsen | Predicting risk of ketosis in dairy cows using in-line measurements of β-hydroxybutyrate: A biological model[END_REF], the development of a real-time EB body method is feasible. Within the EB body method, there are several constants that should not be regarded as universal; for example, the constants (a and b) for converting BCS to body fatness (g of lipid/g of EBW) depend on the BCS scale being used. In the present study, we used the values 0.05 (a) and 0.10 (b) from (Friggens et al., 2007a). However, in a real-time model, it could be envisaged that these constants could be optimized locally by incorporating information from the local relationship between BCS and BW. Further, in a real-time model, using the previous measures in the time-series, it would be possible to determine cowspecific time points when rates of change in BL and BP shift from negative to positive (the energy requirement coefficients y and z differ according to whether deposition or mobilization of body tissues occurs).

It would be desirable to further evaluate the method on larger, independent data sets to confirm the robustness of the method to differences between breeds and parities, and in particular in relation to diet types. In this context, the 2 assumptions made in the present study concerning GF are of interest. We assumed that GF could be considered as having 2 components; namely, meal-related GF and RGF (Martin and Sauvant, 2010b) and then estimated the meal-related GF by quantile regression using the lower 20% quantile. The adequate removal of the influence of meal-related GF from the BW data is important, because failure to do so inevitably transfers this noise to the profiles of EB body . Because differences in feed composition and differences due to prior feed intake both tend toward zero with time (Martin and Sauvant, 2010b), we also assumed that RGF was a constant proportion (0.26) of LFEBW. Simulation using different values suggested that these assumptions were reasonable, but it would be worth examining the robustness of these assumptions in detail using data from experiments specifically designed to examine these issues.

Finally, the present model estimated EB body during the first 150 DIM, when energy consumption of the growing conceptus is negligible. However, if the full lactation were modeled, the weight of the gravid uterus would need to be subtracted from BW before calculation of EB body . The weight of the gravid uterus can be predicted for the entire gestation period, because equations for doing so already exist (NRC, 2001;Martin and Sauvant, 2010a).

CONCLUSIONS

A method for estimating the energy balance (EB body ) of individual cows based solely on frequent measurements of BW and BCS was developed and tested. The BW measurements were sequentially smoothed to derive milk-and meal-related GF-free BW, thus allowing EB body to be estimated without requiring information on feed intake. The EB body compared well with the traditional energy balance calculated from DMI and MY measures. This method has the potential to provide a valuable on-farm management tool without the necessity for measurements of DMI, feed composition, or MY. Future work should focus on adapting the present method to allow real-time estimation of energy balance.

Figure 1 .

 1 Figure 1. Example of BW (kg) development (dots) relative to elapsed time during a single milking, illustrating how the milk-free BW (horizontal line) was derived as the end-point of cubic spline smoothing (line) of the raw weights.

Figure 2 .

 2 Figure 2. Example of milk-free BW (kg) observations ( ) and the smoothed (quantile regressed; see Materials and Methods section) meal-related gutfill-free BW (line) of 1 cow relative to DIM.

Figure 3 .

 3 Figure 3. Example of BCS observations ( ) and smoothed BCS (line) for 1 cow relative to DIM.

Figure 4 .

 4 Figure 4. Examples of energy balance [EB body ; MJ of effective energy (EE)/d] for 4 cows relative to DIM. Color version available in the online PDF.

Figure 5 .

 5 Figure 5. Average energy balance [EB body ; MJ of effective energy (EE)/d] relative to DIM for 76 cows grouped by (A) breed, (B) parity, (C) diet, and (D) standard deviation.

Figure 6 .

 6 Figure 6. Estimated feed energy content (FEC; MJ of effective energy (EE)/kg of DM] relative to DIM for 75 cows grouped by diet. Lines represent the model FEC iklm = μ + breed i + (cDIM m × diet k ) + cow l + ε iklm .

Table 1 .

 1 Milk yield, milk fat, milk protein, DMI, and smoothed BW for the 76 cows grouped by breed and diet, based on 1,108 observations (SD in parentheses)

	Breed	Diet 1	n	Milk yield (kg/d)	Milk fat (%)	Milk protein (%)	DMI (kg/d)	BW (kg)
	Danish Holstein	TMR 1	34	34.4 (7.8)	3.5 (0.5)	3.2 (0.3)	19.2 (3.6)	559 (66)
	Danish Holstein	TMR 2	23	32.0 (8.9)	3.7 (0.6)	3.3 (0.2)	18.5 (2.8)	546 (49)
	Jersey	TMR 1	10	24.5 (3.7)	5.1 (0.6)	3.9 (0.3)	16.8 (3.3)	418 (54)
	Jersey	TMR 2	9	20.5 (4.3)	5.4 (0.7)	4.2 (0.3)	16.0 (3.8)	389 (29)

TMR 1 was a glycerol-rich diet (15% of DM was glycerol, 7% was wheat bran and soybean meal); TMR

was a whole grain-rich diet (22% of DM was whole grain NaOH-treated wheat).

Journal of Dairy Science Vol. 95 No. 4, 2012

ACKNOWLEDGMENTS

This work was part of a project "In-line monitoring technology, biomarkers, sensor technology, risk management, and expert systems" funded by the Danish National Advanced Technology Foundation. The funding body had no involvement with this study. We thank the staff at DCRC for performing the BCS and Connie Middelhede (Department of Animal Science, Aarhus University, Tjele, Denmark) for help in making the raw weight data accessible.


C Vialle

C Sablayrolles

M Lovera

S Jacob

M.-C Huau

M Montrejaud- Vignoles

Monitoring of water quality from roof runoff: Interpretation using multivariate analysis

Keywords: rainwater harvesting system, physicochemical quality, microbiological quality, principal component analysis, cluster analysis

The quality of harvested rainwater used for toilet flushing in a private house in the south-west of France was assessed over a one-year period. Temperature, pH, conductivity, colour, turbidity, anions, cations, alkalinity, total hardness and total organic carbon were screened using standard analytical techniques. Total flora at 22°C and 36°C, total coliforms, Escherichia coli and enterococci were analysed. Overall, the collected rainwater had good physicochemical quality but did not meet the requirements for drinking water. The stored rainwater is characterised by low conductivity, hardness and alkalinity compared to mains water. Three widely used bacterial indicators -total coliforms, E. coli and enterococci -were detected in the majority of samples, indicating microbiological contamination of the water. To elucidate factors affecting the rainwater composition, principal component analysis and cluster analysis were applied to the complete data set of 50 observations. Chemical and microbiological parameters fluctuated during the course of the study, with the highest levels of microbiological contamination observed in roof runoffs collected during the summer. Escherichia coli and enterococci occurred simultaneously, and their presence was linked to precipitation. Runoff quality is also unpredictable because it is sensitive to the weather. Cluster analysis differentiated three clusters: ionic composition, parameters linked with the microbiological load and indicators of faecal contamination. In future surveys, parameters from these three groups will be simultaneously monitored to more accurately characterise roof collected rainwater.

Introduction

Currently, the availability of fresh water is one of the major issues facing the human population. A number of complex factors are driving this issue, including population growth, urbanisation, land use transformation, and pollution. Insufficient availability to drinking water could lead to devastating consequences, such as increasing health problems or social upheaval. Although many solutions have been proposed, there is much interest in the use of roof-collected rainwater. This practice has been used in many countries for thousands of years [START_REF] Pinfold | The bacteriological quality of rainjar water in rural northeast thailand[END_REF] ; [START_REF] Simmons | Contamination of potable roof-collected rainwater in Auckland, New Zealand[END_REF]). Although this solution is attractive from an ecological point of view, it is necessary to measure the quality of harvested rainwater due to the potential for health risks as a result of chemical and microbiological contaminants. Recently, studies in numerous countries, including Thailand, USA, Nigeria, New-Zealand, India, Zambia, Brazil, Canada, Australia, Jordan, New Guinea and South Korea, have investigated the quality of harvested rainwater [START_REF] Pinfold | The bacteriological quality of rainjar water in rural northeast thailand[END_REF] ; [START_REF] Crabtree | The detection of cryptosporidium oocysts and Giardia cysts in cistern water in the U.S. Virgin Islands[END_REF] ; [START_REF] Uba | Rainwater quality from different roof catchments in the Port Harcourt district, rivers state, Nigeria[END_REF] ; [START_REF] Simmons | Contamination of potable roof-collected rainwater in Auckland, New Zealand[END_REF] ; [START_REF] Handia | Potential of rainwater harvesting in urban Zambia[END_REF] ; [START_REF] Kulshrestha | Chemical characteristics of rainwater at an urban site of south-central India[END_REF] ; [START_REF] May | Experimental evaluation of rainwater quality for non-potable applications in the city of Sao Paulo, Brazil[END_REF] ; [START_REF] Al-Khashman | Chemical characteristics of rainwater collected at a western site of Jordan[END_REF] ; [START_REF] Despins | Assessment of rainwater quality from rainwater harvesting systems in Ontario, Canada[END_REF] ; [START_REF] Evans | Extensive bacterial diversity indicates the potential operation of a dynamic micro-ecology within domestic rainwater storage systems[END_REF] ; [START_REF] Horak | Microbial and metal water quality in rain catchments compared with traditional drinking water sources in the East Sepik Province, Papua New Guinea[END_REF] ; [START_REF] Lee | Comparison of the microbiological and chemical characterization of harvested rainwater and reservoir water as alternative water resources[END_REF]). In Europe, rainwater quality assessment was studied by Förster (1998), Förster (1999), [START_REF] Albrechtsen | Microbiological investigations of rainwater and graywater collected for toilet flushing[END_REF], Polowska and al. (2002), Fewtrell and Kay (2007), Melidis and al. (2007), Oesterholt and al. (2007), [START_REF] Sazakli | Rainwater harvesting, quality assessment and utilization in Kefalonia Island, Greece[END_REF], [START_REF] Schriewer | Time focused measurements of roof runoff quality[END_REF], Tsadovski and al. (2010). Although a number of studies have found collected rainwater to be nonpotable, showing unacceptable levels of microbiological contamination and poor physicochemical qualities, "a clear consensus on the quality and health risk associated with roof-collected rain-water has not been reached" ( [START_REF] Evans | Wind, rain and bacteria: the effect of weather on the microbial composition of roof-harvested rainwater[END_REF]). This lack of consensus is likely due to the fact that the qualities of harvested and stored rainwater are dependent on a number of factors, including geographical location, catchment area, storage time, handling and management of the water ( [START_REF] Vazquez | A rainwater quality monitoring network: a preliminary study of the composition of rainwater in Galicia (NW Spain)[END_REF] ; [START_REF] Chang | Roofing as a source of nonpoint water pollution[END_REF] ; [START_REF] Zhu | Quality issues harvested rainwater in arid and semiarid Loess Plateau of nothern China[END_REF] ; [START_REF] Evans | Identifying the major influences on the microbial composition of roof harvested rainwater and the implications for water quality[END_REF] ; [START_REF] Huston | Characterisation of atmospheric deposition as a source of contaminants in urban rainwater tanks[END_REF] ; [START_REF] Lye | Rooftop runoff as a source of contamination: A review[END_REF]). Like most countries, France must spare its water resources and, for several years, has taken an interest in harvesting rainwater for domestic use. Despite reluctance from authorities (C.S.H.P. F, 2006), the increasing demand from private customers has prompted authorization of the use of rainwater for certain applications. Currently, French law prohibits the use of harvested rainwater for drinking, showering or bathing, or washing clothes (Decree of [START_REF]Relating to rainwater harvesting and their use at the interior and the outside of buildings[END_REF]. In recent years, the application of multivariate analysis to complex data sets has enjoying a high level of scientific interest. One of the main advantages of these techniques, such as principal component analysis (PCA) and cluster analysis (CA), is the ability to analyse large datasets containing many variables and experimental units. PCA and CA identify groups and sets of variables with similar properties and may allow us to simplify our description of observations by finding the structure or patterns in chaotic or confusing datasets. Additionally, these techniques allow the analysis of data from non-homogeneous variables. Thus, multivariate methods are now used in a variety of scientific disciplines. In the field of rainwater, they have been applied to the study of precipitations composition mainly in ions and sometimes in metals [START_REF] Zhang | Application of principal component analysis to the interpretation of rainwater compositional data[END_REF] ; [START_REF] Hu | Chemical characterization of rainwater in Singapore[END_REF] ; [START_REF] Simeonov | Multivariate statistical study of simultaneously monitored cloud water, aerosol and rainwater data from different elevation levels in an alpine valley ( Achenkirch, Tyrol, Austria)[END_REF] ; [START_REF] Vazquez | A rainwater quality monitoring network: a preliminary study of the composition of rainwater in Galicia (NW Spain)[END_REF] ; [START_REF] Zunckel | Rainwater composition in northeast Uruguay[END_REF] ; [START_REF] Astel | Application of PCA and time series analysis in studies of precipitation in Tricity (Poland)[END_REF] ; [START_REF] Khare | Chemical characterization of rainwater at a developing urban habitat of Northern India[END_REF] ; [START_REF] Baez | Chemical composition of rainwater collected at a southwest site of Mexico City, Mexico[END_REF]) or to the study of rainwater monitoring network [START_REF] Mantovan | Characterization of rainwater quality from the Venice region network using multiway data analysis[END_REF] ; [START_REF] Ouyang | Evaluation of river water quality monitoring stations by principal component analysis[END_REF]. By contrast, our study concerned the characterization of stored roof-collected rainwater and the simultaneous analysis of chemical, physical and microbiological parameters. The purpose of the present study is to monitor physicochemical and microbiological parameters of collected rainwater and to use PCA and CA to further characterise associations present in the complete data set. Rainwater was collected over a one-year period using a commercially available system installed in south-western France.

Material and methods

Sampling site

Rainwater harvesting system

A commercially available domestic rainwater collection system (Sotralentz Habitat) was installed in a rural village in south-western France. The house was occupied by a family consisting of two parents and two children. The average rainfall in this region is 760 mm, and the average temperatures range from 7.9 -18.3 °C. In the system installed, rainwater is first collected from a 204 m 2 surface area of tiled roof and then channelled via open zinc gutters through pipes to an underground PEHD storage tank with a 5 m 3 capacity. Prior to entering the tank, the water is passed through a mesh. In the event of an overflow, excess water is fed into a nearby canal. A submerged intake with an inlet filter attached to a float is used to pump water inside the house. Prior to use, collected rainwater is treated by being passed through a physical filter (25µm) and an activated carbon filter. When insufficient water is available in the tank, a probe activates a valve to allow pumping from a backup drinking water tank. The collected rainwater could be used for toilet flushing and watering gardens; it supplied water for two WCs and an outside tap. A schematic of the rainwater collection system is shown in Figure 1.

Figure 1. Schematic of the rainwater harvesting system installed in south-western France.

Sample collection

Sampling was carried out weekly from January 2009 to January 2010. To monitor water quality, grab samples were taken from the surface water in the tank each week.

The sampling was performed using a sampling rod and a beaker. Prior to sampling, the beaker was disinfected with ethanol, rinsed once with ultra high quality water and then rinsed twice with tank water. Samples were stored in polyethylene bottles for chemical analysis or individual sterile bottles for microbiological analysis. Temperature, pH and conductivity were measured in situ, and the sample was stored in a chilled cold-box during transportation to the laboratory, where samples were stored at 4°C. Microbiological analyses were conducted within 24 h. Samples collected to assess chemical parameters were frozen for later analysis.

Analytical determinations

Chemical analysis

Samples were measured for pH, conductivity, colour, turbidity, total organic carbon (TOC), ionic composition (Cl -, SO 4 2-, NO 3 -, PO 4 3-,Mg 2+ , Ca 2+ , Na + , K + , NH 4 + ), total hardness, simple alkalimetric title (AT), complete alkalimetric title (CAT). Samples were analysed in accordance with norms shown in Table 1. Ionic composition was analysed with ion chromatography (Dionex, AG/AS 18, ICS 2000 for anions and CG/CS 12, ICS 3000 for cations).

Table1. Physico-chemical parameters analysed

Microbiological analysis

All samples were examined for the three widely used bacterial indicators using the relevant ISO (International Organization for Standardization) standards: ISO 9308-1 for total coliforms and Escherichia coli, and ISO 7899-2 for enterococci, as well as ISO 6222 for total flora at 22°C and 36°C.

Multivariate data analysis

In this study, multivariate chemometric techniques were performed using the commercial software XL stat.

Principal component analysis

Principal Component Analysis (PCA) is one of the most applied approaches in the environmetrics to study data structures. It is aimed at finding and interpreting hidden complex and casually determined relationships between dataset features. This is accomplished by studying the data structure in a reduced dimension while retaining the maximum amount of variability present in the data. To do this, it is necessary to estimate the number of significant components present in the data. More precisely, a matrix of pairwise correlations among parameters is decomposed into eigenvectors, which, in turn, are sorted in descending order of their corresponding eigenvalues. At this point, the raw data are generally unsuitable for statistical analyses due to differences in the sizes of the variables. Mathematically, PCA normally involves three major steps: 1) the standardisation of measurements to ensure that they have equal weights in the analysis by autoscaling the data to produce new variables, where the mean is equal to zero and the standard deviation is equal to the unit; 2) calculation of the covariance matrix by identifying the eigenvalues and their corresponding eigenvectors; and 3) the elimination of components that account only for a small proportion of the variation in data sets.

Cluster analysis (CA)

Cluster Analysis (CA) nicely complements PCA. It was used to search for natural groupings among objects and discover latent structures present in the data. Analysed parameters were sorted into groups, or clusters, so that the degree of association is strong between members of different clusters. Prior to CA, the descriptor variables were block standardised by range to avoid effects of scale or units on the distance measurements. Hierarchical agglomerative CA was performed on the normalised data set with the Ward's method, using Euclidean distances as a measure of similarity.

Results and discussion

Descriptive statistics

Prior to multivariate analysis, univariate descriptive statistics were used to compare the measured variables with French drinking water guidelines (Decree of [START_REF]Relating to rainwater harvesting and their use at the interior and the outside of buildings[END_REF]. Indeed as it was impossible to present the complete data set which corresponds to 23 parameters for 55 samplings, minimum, maximum, mean, median and standard deviation were used to describe it (Table 2). Values less than the quantification limit were considered to be zero for statistical calculations. The pH range of collected water was 5.6 -10.4. Extreme alkaline values were observed after strong weather events. For example, the highest pH of 10.4 was recorded after a violent storm and remained elevated for five weeks before returning to a slightly acidic condition (Figure 2). Outside of these weather-related spikes, the pH range was 5.6 -6.9. By comparison, the literature for Europe has reported the following pH ranges for runoff water: 6.0 -8.2 [START_REF] Villarreal | Analysis of a rainwater collection system for domestic water supply in Ringdansen, Norrköping, Sweden[END_REF]), 7.6 -8.8 [START_REF] Sazakli | Rainwater harvesting, quality assessment and utilization in Kefalonia Island, Greece[END_REF]) and 5.8 -8.4 [START_REF] Schriewer | Time focused measurements of roof runoff quality[END_REF]). Half of the samples collected in this study exceed the drinking water limits for colour (15 mg Pt/L) and turbidity (2 NTU). Ion concentrations were low, with 89 % of conductivity values being below 100 µS.cm -1 . This finding indicates that harvested rainwater had a low level of mineralisation. Concentrations in ion comply with the drinking water guidelines available, except for ammonia, which was often detected at unacceptably high levels. The microbiological composition of the tank water varied over the course of the year. Total flora is a measure of the total bacterial load. At 22 °C, bacterial counts ranged from 10 to 6.32x10 5 organisms per mL. Almost all samples were contaminated with coliform bacteria (i.e., they exceeded zero organisms per 100 mL of water). Two faecal indicators were also monitored and showed varying degrees of contamination. Roof-collected rainwater often showed high levels of contamination with enterococci, as can be seen from the fact that the maximum value exceeded 10,000 CFU per 100 mL of water. The majority of samples (79 %) tested positive for E. coli, an indicator of faecal contamination. E. coli and enterococci were simultaneously present in samples, always with enterococci having the higher concentrations (Figure 3). Although these bacteria are unable to reproduce in water, enterococci has a better survival ability in water than E. coli. Three widely used bacterial indicators, total coliform, E. coli and enterococci, were detected in the majority of samples. In concordance with previous studies (Simmons 2007)), our results show that roof rainwater runoff is not suitable for human consumption due to the high levels of microbiological contamination within it. Whereas roof-collected rainwater, in general, meets the classical parameters for drinking water in terms of physico-chemistry, the bacterial contamination resent in the collected samples was above acceptable limits. As a result, it must be recommended to use a system equipped of disinfection. In addition, it must be highlighted that no first-flush diversion was used in this study. Now such a system could permit to decrease concentrations of some of the tested water quality parameters [START_REF] Mendez | The effect of roofing material on the quality of harvested rainwater[END_REF]. present in samples, always with enterococci having the higher concentrations

Multivariate methods

A starting data matrix, with columns representing the different samplings (observations) and rows corresponding to the measured parameters (variables), was constructed. The variability of total coliform load was excluded because at least thirteen results were unusable due to the presence of an interfering flora in the sample.

It must be highlighted descriptive statistics of the dataset were already presented in table 2 but multivariate analysis were performed using primary dataset. A total of 50 complete observations (no missing values across the 22 variables) were thus selected for further analysis with Principal Component Analysis (PCA) and Cluster Analysis (CA). In PCA, the number of components is equal to the number of variables. A component, however, is comprised not only of a single variable but all of the variables used in the study. The PCA analysis showed that of the 22 components, the first component (F1) accounted for about 28.5 % of the total variance, the second component (F2) accounted for about 20.4 % of the total variance and the third component (F3) accounted for about 11.1 % of the total variance of the dataset. Table 3 gives the loadings for the three first components and square cosines are presented in Figure 4. A variable is increasingly well represented by a component as the corresponding value of the square cosine approaches the unit. Almost all variables are well represented by the first three components, F1, F2 or F3. Only total flora at 22°C, and AT could have been better represented by a different component. Our discussion, therefore, will focus principally on the three principal components that, collectively, explain 60.0 % of the total variance of the dataset. This reduced the dimensionality of the total data from 22 to 3 (an 86.3 % reduction) and resulted in a 40.0 % loss of information contained in the dimensions. The variables that primarily contributed to the first eigenvector were pH, conductivity, hardness, calcium and potassium. Thus, the first principal component can be interpreted as an ionic component. The second eigenvector was mainly related to organic load, with the most significant variables being temperature, total organic carbon, and ammonium and phosphate values. The third eigenvector represented faecal contamination by enterococci and E. coli (Figure 4). Cluster A is the ionic component previously described as the first eigenvector in PCA. The level of dissimilarity detected between cluster B and C justified that their association appeared separately in the second and third eigenvectors in PCA. There was adequate agreement between results obtained by unsupervised PCA and CA to confirm the conclusions made over the complete dataset.

Figure 5. A dendrogram obtained by application of the Ward's method. -Three clusters were identified corresponding to the three principal components identified with PCA.

To elucidate the influence of collection date on stored rainwater composition, different observations were represented in the planes F1 through F2 (Figure 6). Sample points corresponding to the January 2009 storm event were differentiated from the central scatter plot (27/01/09, 10/02/09, 17/02/09, 24/02/09). These points are high on F1, the ionic component. In fact, the January 2009 storm strongly affected the collected water parameters, particularly in terms of pH. Samplings that occurred in summer showed high F2 values, corresponding to the bacterial load. Summer months have higher temperatures and less runoff water to refill the tank, thus, explaining the higher levels of biological contamination. Selection of three eigenvectors also permitted direct data evaluation via a three-dimensional plot (Figure 7). This representation illustrates the variability observed throughout the one year period that the roof runoff was collected.

Comment citer ce document : On planes F1 through F3, E. coli and enterococci were well represented and appeared to be positively correlated (Figure 4). In order to investigate this correlation and to elucidate the origin of these two faecal indicators, an additional ACP was realised using daily pluviometry as extra parameter which was only available beginning in March 2009. Sample points corresponding to the January 2009 storm event were thus excluded. The AT was also removed from analysis because it was generally below the limit of quantification. Thus, the new autoscaled matrix was comprised of 22 parameters and 43 observations. The presence of E. coli and enterococci were significantly correlated with each other. The Pearson's coefficient was equal to 0.989, with a corresponding regression coefficient (R 2 ) of 0.979. In addition, the results show these two faecal indicators were significantly correlated with pluviometry. The linear Pearson's coefficient (linear regression coefficient) was 0.798 (R 2 =0.637) for E. coli and 0.841(R 2 =0.707) for enterococci. It should be noted that these correlations were strongly influenced by a weather event on March 11 th , 2009, during which 39 mm of rain fell in one day. At this time, the bacterial loads were 33,000 CFU per 100 mL for E. coli and 30,000 CFU per 100mL for enterococci (Figure 8). As illustrated in the dendrogram, these results were confirmed in the cluster analysis (Figure 9).

Conclusions

The present work presents results concerning the quality of stored roof runoff. For each sample, we measured pH, conductivity, colour, turbidity, total organic carbon, anions, cations, total hardness, AT, CAT, E. coli, enterococci, and total flora at both 22°C and 36°C. Univariate descriptive statistics for the observed variables were conducted for each sampling event. Several conclusions may be drawn from this study but it must be reminded it is based on a limited data set: the performance of a rainwater collection system was monitored weekly over a period of one year.

Although harvested rainwater was found to be of good physicochemical quality, it did not meet drinking water standards. These findings are congruent with a number of other studies indicating that roof-collected rainwater makes poor quality drinking water due to high levels of bacterial contamination.

An effort was made to extract more information from the datasets through the use of the multivariate analysis techniques. PCA and CA revealed some specific features of the data structure. Three principal components were identified which, collectively, accounted for 60.0% of the total variance; the first component was identified as the ionic component, the second component was linked with organic load and the third component represented faecal contamination. PCA results were confirmed with CA. Three clusters of variables were detected, corresponding to the three previously identified components. It is necessary to monitor at least one parameter of each of these three groups to correctly characterise roof-collected water.

The great variability of roof runoff quality over the course of the study was illustrated with a three-dimensional plot. We were able to distinguish samples that were influenced by a storm event primarily through the first component, whereas samplings obtained in summer months were discernable due to high levels of microbial contamination. It is known rainfall is characterised by its temporal and spatial distribution and its unpredictability. Most importantly, we found that the quality of roof runoff was also unpredictable over a year at the same location. This great variability is coherent with recommendation of a system equipped with a disinfection.

At the same time, E. coli and enterococci were simultaneously present in collected water samples, and their presence was positively correlated with the daily pluviometry. These data suggest that runoff from the roof seeded the tank with faecal contaminants and that bacteriological quality degrades during storage. As a result a first-flush diversion could improve the quality of harvested rainwater.

  Comment citer ce document : Vialle, C. (Auteur de correspondance), Sablayrolles, C., Lovera, M., Jacob, S., Huau, M.-C., Montréjaud Vignoles, M. (2011). Monitoring of water quality from roof runoff: Interpretation using multivariate analysis. Water Research, 45 (12), 3765-3775. , DOI : 10.1016/j.watres.2011.04.029 6/16 and al. (2001) ; Albrechtsen (2002) ; Blangis and Legube (2007) ; Nolde (2007) ; Sazakli and al. (

Figure 2 .

 2 Figure 2. pH values observed during the sampling period (January 2009 -January 2010). -The highest pH of 10.4 was recorded In January after a violent storm and remained elevated for five weeks before returning to a slightly acidic condition

  These 50 observations were partitioned into the following groups: 8 observations in winter 2009, 12 observations in spring 2010, 12 observations in summer 2010, 14 observations in autumn 2010 and 4 observations in winter 2010. Comment citer ce document : Vialle, C. (Auteur de correspondance), Sablayrolles, C., Lovera, M., Jacob, S., Huau, M.-C., Montréjaud Vignoles, M. (2011). Monitoring of water quality from roof runoff: Interpretation using multivariate analysis. Water Research, 45 (12), 3765-3775. , DOI : 10.1016/j.watres.2011.04.029 8/16

Figure 4 .

 4 Figure 4. The square cosines for all variables in a) components F1 and F2 and b) components F1 and F3. -A variable is increasingly well represented by a component as the corresponding value of the square cosine approaches the unit. Almost all variables are well represented by the first three components.

  Figure 6. A two-dimensional plot of the 50 observations in F1 and F2. -Su=Summer; A=Autumn, W=Winter, S=Spring -Observations corresponding to the storm event of January 2009 and summer collection months can be differentiated from the central scatter plot.

Figure 7 .

 7 Figure 7. A three-dimensional plot of the 50 observations in F1, F2 and F3. -Su=Summer; A=Autumn, W=Winter, S=Spring -Observations corresponding to the storm event of January 2009 and summer collection months can be differentiated from the central scatter plot.

  Comment citer ce document : Vialle, C. (Auteur de correspondance), Sablayrolles, C., Lovera, M., Jacob, S., Huau, M.-C., Montréjaud Vignoles, M. (2011). Monitoring of water quality from roof runoff: Interpretation using multivariate analysis. Water Research, 45 (12), 3765-3775. , DOI : 10.1016/j.watres.2011.04.029 13/16

Figure 8 .

 8 Figure 8. Daily pluviometry and concentrations of E. coli and enterococci observed during the period from March 2009 through January 2010 -The two faecal indicators were significantly correlated with pluviometry.

Figure 9 .

 9 Figure 9. The dendrogram obtained applying the Ward's method.-Daily pluviometry is included, and AT is excluded.

  Comment citer ce document : Vialle, C. (Auteur de correspondance), Sablayrolles, C., Lovera, M., Jacob, S., Huau, M.-C., Montréjaud Vignoles, M. (2011). Monitoring of water quality from roof runoff: Interpretation using multivariate analysis. Water Research, 45 (12), 3765-3775. , DOI : 10.1016/j.watres.2011.04.029 15/16

  Comment

	Parameter				Norm
	pH					NF T 90-008
	Conductivity				NF EN 27888
	Turbidity				NF EN ISO 7027
	Cl -, SO 4	2-, NO 3	-, PO 4	3-		NF EN ISO 10304-1
	Mg 2+ , Ca 2+ , Na + , K + , NH 4	+	NF EN ISO 14911
	Colour					NF EN ISO 7887
	Total organic carbon (TOC)	NF EN 1484
	Total hardness				NF EN ISO 14911
	Alkalinity (AT, TAC)		NF EN ISO 9963-1

citer ce document : Vialle, C. (Auteur de correspondance), Sablayrolles, C., Lovera, M., Jacob, S., Huau, M.-C., Montréjaud Vignoles, M. (2011). Monitoring of water quality from roof runoff: Interpretation using multivariate analysis. Water Research, 45 (12), 3765-3775. , DOI : 10.1016/j.watres.2011.04.029 5/16

Table 2 .

 2 Descriptive statistics for the dataset

										French
	Variables	Units	Obser-vations	Minimum Maximum Mean Median	Standard deviation	Drinking Water
										Guidelines
	pH		-	55	5.6	10.4	6.5	6.2	1.1	6.5 to 9
	Temperature °C	55	7.8	22.4	14.9	13.5	4.8	25
	Conductivity µS.cm -1 55	13.5	235.0	56.2	38.2	45.5	180 to 1000
	Colour	mg Pt.L -1 55	<5	39	18	19	10	2
	Turbidity	NTU	53	0.50	6.1	2.4	2.0	1.4	15
	TOC	mg.L -1	55	0.50	5.1	2.3	2.2	1.0
	hardness	mmol.L -1 55	<0.01	0.58	0.16	0.11	0.13
	AT		mmol.L -1 55	<0.20	0.9	0.10	<0.20	0.20
	CAT	mmol.L -1 55	<0.40	1.1	0.30	0.30	0.30
	Cl -		mg.L -1	54	0.55	4.0	1.9	1.7	0.98	250
	2--NO 3 SO 4 3-PO 4 Mg 2+	mg.L -1 mg.L -1 mg.L -1 mg.L -1	54 54 54 54	0.50 0.54 <0.10 <0.10	6.6 7.8 0.54 0.71	1.9 2.8 0.17 0.27	1.8 2.4 0.19 0.24	0.92 1.6 0.14 0.15	250 50
	Ca 2+	mg.L -1	54	1.0	19	4.4	2.9	4.0
	Na +		mg.L -1	54	0.30	2.9	1.1	0.93	0.59	200
	K +		mg.L -1	54	0.15	4.9	1.2	0.78	1.1
	NH 4	+	mg.L -1	54	<0.10	1.7	0.58	0.32	0.57	0.10
	Total coliforms	ufc per 100mL	40	<10	>10 000	656	40	2 189
	Escherichia Coli	ufc per 100mL	53	<10	5 500	148	2	757
	Enterococci	ufc per 100mL	54	<10	>10 000	322	45	1 359
	Total flora at 22°C	ufc per mL	52	10	632 000	45 486 9 700	108 954
	Total flora at 36°C	ufc per mL	51	25	368 000	26 651 4 500	67 906

Comment citer ce document : Vialle, C. (Auteur de correspondance), Sablayrolles, C., Lovera, M., Jacob, S., Huau, M.-C., Montréjaud Vignoles, M. (2011). Monitoring of water quality from roof runoff: Interpretation using multivariate analysis. Water Research, 45 (12), 3765-3775. , DOI : 10.1016/j.watres.2011.04.029 7/16

Table 3 .

 3 Loadings of the first three eigenvectors, F1, F2 and F3, in the total data set.

	Variable	F1	F2	F3
	pH		0,318	-0,138	0,219
	Temperature	-0,104	0,377	0,065
	Conductivity	0,335	-0,048	0,089
	Coulour	-0,014	0,235	0,026
	Turbidity	0,178	0,265	0,172
	TOC	0,156	0,400	0,062
	hardness	0,351	-0,062	0,120
	AT		0,115	-0,155	0,184
	CAT	0,234	0,049	0,190
	Cl -		0,256	-0,083	-0,146
	2--NO 3 SO 4 3-PO 4 Mg 2+	0,158 0,149 0,011 0,225	0,077 0,001 0,384 0,193	-0,273 -0,316 -0,130 -0,187
	Ca 2+	0,368	-0,074	0,102
	Na +	0,270	-0,102	-0,147
	K +		0,358	-0,018	0,096
	NH 4	+	0,041	0,414	0,085
	Escherichia Coli	-0,117	-0,110	0,455
	Enterococci	-0,113	-0,099	0,447
	Total flora at 22°C	-0,013	0,194	0,284
	Total flora at 36°C	0,015	0,276	0,197
	Eignevalue (%)	28.47	20.40	11.13

Comment citer ce document : Vialle, C. (Auteur de correspondance), Sablayrolles, C., Lovera, M., Jacob, S., Huau, M.-C., Montréjaud Vignoles, M. (2011). Monitoring of water quality from roof runoff: Interpretation using multivariate analysis. Water Research, 45 (12), 3765-3775. , DOI : 10.1016/j.watres.2011.04.029 9/16

  Comment citer ce document : Vialle, C. (Auteur de correspondance), Sablayrolles, C., Lovera, M., Jacob, S., Huau, M.-C., Montréjaud Vignoles, M. (2011). Monitoring of water quality from roof runoff: Interpretation using multivariate analysis. Water Research, 45 (12), 3765-3775. , DOI : 10.1016/j.watres.2011.04.029

	12/16

Table 4 .

 4 Pearson's correlations between different variables from March 2009 to January 2010.

																	E.		TF	TF
	Variables	pH	Temp. Cond. Colour Turb. TOC	Hard. CAT	Cl -	SO4 2-	NO3 -	PO4 3-	Mg 2+	Ca 2+	Na +	K +	NH4 +	Coli	Entero.	22°C	36°C	Pluvio.
	pH	1
	Temperature	-0.035	1
	Conductivity	0.451	0.093	1
	Coulour	0.216	0.361	0.087	1
	Turbidity	0.490	0.439	0.373	0.269	1
	TOC	0.410	0.680	0.474	0.353	0.797 1
	hardness	0.675	0.121	0.650	0.342	0.424 0.591 1
	CAT	0,307	0,215	0,278	0,343	0,217 0,283 0,503 1
	Cl -	0.452	-0.352 0.422	-0.059	0.073 0.088 0.467 0,145 1
	SO4 2-	0.376	0.087	0.645	-0.144	0.176 0.309 0.276 -0,049 0.273 1
	NO3 -	0.156	-0.209 0.440	0.205	-0.133 0.097 0.304 -0,015 0.359 0.291 1
	PO4 3-	0.143	0.626	0.257	0.432	0.423 0.713 0.314 0,214 -0.018 0.198 0.264 1
	Mg 2+	0.578	0.226	0.593	0.339	0.608 0.694 0.752 0,418 0.387 0.316 0.335 0.578 1
	Ca 2+	0.687	-0.095 0.660	0.291	0.292 0.395 0.795 0,434 0.611 0.300 0.508 0.266 0.734 1
	Na +	0.490	-0.216 0.574	-0.182	0.054 0.068 0.386 0,092 0.682 0.697 0.213 -0.025 0.286 0.487 1
	K +	0.546	-0.093 0.624	0.339	0.280 0.426 0.664 0,333 0.577 0.265 0.623 0.387 0.623 0.883 0.389 1
	NH4 +	0.211	0.642	0.316	0.315	0.684 0.821 0.380 0,249 0.022 0.115 -0.145 0.651 0.449 0.244 -0.064 0.394 1
	Escherichia
	Coli	0.111	-0.096 -0.208 -0.267	-0.102 -0.200 -0.144 -0,095 -0.100 -0.252 -0.257 -0.257 -0.314 -0.182 -0.093 -0.188 -0.177 1
	Enterococci	0.101	-0.119 -0.180 -0.270	-0.087 -0.170 -0.131 -0,152 -0.082 -0.240 -0.208 -0.229 -0.290 -0.175 -0.100 -0.157 -0.152 0.989 1
	Total flora at
	22°C	0.132	0.153	-0.020 -0.003	0.217 0.264 0.016 0,046 0.089 0.017 0.035 0.215 0.063 0.029 -0.022 0.175 0.331 0.314 0.340	1
	Total flora at
	36°C	0.182	0.300	0.081	0.076	0.358 0.430 0.130 0,169 0.082 0.071 0.021 0.314 0.213 0.112 -0.023 0.225 0.473 -0.007 0.007	0.789 1
	Pluviometry	0.049	-0.203 -0.148 -0.148	-0.123 -0.137 -0.088 -0,234 -0.057 -0.214 -0.001 -0.108 -0.241 -0.142 -0.122 0.025 -0.041 0.798 0.841	0.381 0.084 1

Comment citer ce document : Vialle, C. (Auteur de correspondance), Sablayrolles, C., Lovera, M., Jacob, S., Huau, M.-C., Montréjaud Vignoles, M. (2011). Monitoring of water quality from roof runoff: Interpretation using multivariate analysis. Water Research, 45 (12), 3765-3775. , DOI : 10.1016/j.watres.2011.04.029 14/16

Acknowledgement

The authors would like to thank Sotralentz Habitat for their provision of rainwaterharvesting equipment.