# Frequency Analysis of the Loire River water Total Suspended Solid and Electrical Conductivity (Orléans, France)

Mohammed Rashid Al-Juhaishi, Fabrice Muller, Mikael Motelica-Heino

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Mohammed Rashid Al-Juhaishi, Fabrice Muller, Mikael Motelica-Heino. Frequency Analysis of the Loire River water Total Suspended Solid and Electrical Conductivity (Orléans, France). IOP Conference Series: Earth and Environmental Science, 1374, 2024, 10.1088/1755-1315/1374/1/012071. insu-04676493

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# Frequency Analysis of the Loire River water Total Suspended Solid and Electrical Conductivity (Orléans, France)

To cite this article: Mohammed Rashid Al-Juhaishi et al 2024 IOP Conf. Ser.: Earth Environ. Sci. 1374 012071

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# Frequency Analysis of the Loire River water Total Suspended Solid and Electrical Conductivity (Orléans, France)

AL-JUHAISHI Mohammed Rashid<fnref n="1" />, a*, Muller Fabrice<fnref n="2" />, b, and MOTELICA-HEINO Mikael<fnref n="3" />, c

**Abstract.** In this research, different statistical probability distributions are presented to model the total suspended solids (TSS) and electrical conductivity (EC) at two monitoring stations, Along the path of the Loire River France. These monitoring stations are Jargeau and Meung-sur-Loire. For each of these station data of the two variables are measured as a monthly series during the period 2001 to 2021. The proposed fitted statistical probability distributions are the Normal, Log-normal, Weibull, Exponential and Two parameters Gamma. The Kolmogorov-Smirnov test is used for the goodness-of-fit to select the best probability distribution from among these five tried distributions for each of the stations. The data sample is divided into two sub-samples, a fitting model sub-sample as 70 % of the data, and a validation sub-sample as the remaining 30%. The results show that the TSS at Loire a Meung-sur-Loire station has two distributions with same value of the test statistics, SIG. In these cases, the t and F tests are used to select the best-fit distribution. The Log Normal (13.71, 0.95) is found to be the best fit distribution for TSS for Jargeau station with SIG value of 0.35 while the Weibull (282.911, 8.206) with SIG value of 0.877 is the best fit for EC for the same station. For the Meung-sur-Loire station the Weibull (19.49, 1.18) and (299.40, 7.50) are the best fit distributions for the TSS and EC with test SIG values 0.75, 0.99 respectively. The best fit distribution for each station is used to generate three series of data which are tested against the 30% validation data. The Kolmogorov-Smirnov test among the three generated series with the validation confirms that these fitted models can generate data that has the same frequency of occurrence of that of the observed data.

**Keywords:** Non-parametric test, Kolmogorov-Smirnov test, water quality, goodness-of-fit test, La Loire River.

## 1. INTRODUCTION

Human activities, increasing production, urban expansion and disposal of chemical products may cause an inevitable impact on human health and the ecosystem. Therefore, this expansion acting as a key index to planning of an efficient treatment plant, developed water distribution network, and an efficient wastewater treatment plant. The constructions of such projects require a lot of future data so the decision makers need a validated forecasting model to know the behavior of certain parameters in the future. Frequency analysis is considered as one of the most methods used in the domain of water resources to generate future data using a validate forecasting model based on a historical series. The amount of rainfall is an important factor in the designing of hydraulic and other structures and in planning for floods and drought events. The availability of a model that predicts the most probable amount of rainfall is very useful for planning and operation of socio-economic systems e.g., management of water resources, protection of floods, irrigation projects, and many others. It provides the decision makers with information about the consequences of precipitation anomalies. Future rainfall data can be predicted depending on past data of rainfall events; therefore, the understanding of the patterns and the distributions of historical records is considered to have a significant role in the development and conservation of natural resources.

In engineering hydrology, observed past data can be used for fitting different frequency distributions and select the best fit one. This is considered an important task that can be used to predict the probability of future possible selected event [1-3]. However, a lot of estimation methods is adopted for this strategy so it not a simple path [4, 5]. Sharma et al. [6] selected the Gamma distribution to be the best fit for rainfall data of different stations in India. Khudri and Sadia [7] found that the Gamma four-parameter distribution had the ability to fit 50% of the stations in Bangladesh, while for the other 50% of the stations no distribution was capable to fit their rainfall data. Mandal et al. [8] found that the normal (N) distribution was the best-fit frequency distribution for the annual, summer seasons and post-monsoon rainfall data in Sagar Island Bay of Bengal. For the same area they found that the Lognormal (LN2), Pearson type 5, and Weibull (W2) were best fit for the pre-monsoon, winter seasons and monsoon respectively. Amin et al. [9] indicated that the best-fit distribution in the northern regions of Pakistan for daily sample was the log normal type 3 to compute maximum annual. Smith et al. [10] developed frequency analysis methods which is implemented based on high-resolution radar rainfall data sets

<figure><img src="image_4.png" /></figure>

<footnote n="1">¹Department of Water Resources Engineering, University of Baghdad, Baghdad Iraq.</footnote>

<footnote n="2">²ICMN Nanostructure Materials Confinement Interfaces CNRS UMR7374, University of Orléans, Orléans, France.</footnote>

<footnote n="3">³ISTO Earth Sciences Institute of Orléans CNRS UMR 7327, University of Orléans, Orléans, France.</footnote>

<footnote>a@m.rashid@coeng.uobaghdad.edu.iq, b@fabrice.mller@univ-orleans.fr, c@mikael.motelica@univ-orleans.fr</footnote>

<footnote>*Corresponding author</footnote>
for 22-year for the Baltimore study region. They concluded that sub-daily rainfall extremes are only weakly related to daily extremes, pointing to difficulties in inferring climatological properties of sub-daily rainfall from daily rainfall analyses. This study focuses on the best-fit distribution for the TSS and EC of two hydrological monitoring stations located along the path of Loire River in France.

## 2. THEORETICAL BASIS

In this study, different statistical frequency distributions are used to fit the monthly records of TSS and EC of the two meteorological stations mentioned above. SPSS v26 software is used to estimate the parameters and to apply the best of fit test Kolmogorov-Smirnov test to decide which distributed is the best. Following is the mathematical description of the five distributions used:

### 2.1. Normal Distribution

For this distribution the probability density function (pdf), f(x) for a normal random variable x is expressed as [1,11].

$$f(x) = \frac{1}{\sigma\sqrt{2\pi}} \exp \left[ -\frac{1}{2\sigma^2} (x - \mu)^2 \right] \quad (1)$$

Where: μ is the mean (Location) and σ is the standard deviation (Scale).

### 2.2. Log-Normal Distribution

The probability density function (pdf) of this distribution is expressed as follow[1, 11].

$$f(x) = \frac{1}{x\sigma\sqrt{2\pi}} \exp \left[ -\frac{1}{2\sigma^2} (\log x - \mu)^2 \right] \quad (2)$$

Where: μ the mean value of log(x) Scale and σ is the standard deviation (Shape parameter).

### 2.3. Exponential Distribution

The probability density function (pdf) of this distribution is expressed as[1, 11]:

$$f(x) = \frac{1}{\mu} \exp \left[ \frac{x}{\mu} \right] \quad (3)$$

In which μ is the distribution's parameter.

### 2.4. Weibull Distribution

The probability density function (pdf) of Weibull distribution is expressed as follow [1, 11]:

$$f(x) = \frac{a}{b^{-a}} x^{a-1} \exp \left[ -\left( \frac{x}{b} \right)^{a} \right] \quad (4)$$

In which (a) is the Shape parameter and (b) is the Scale parameter.

### 2.5. Gamma Distribution PDF

$$f(x) = \frac{a}{b^a} \left(\frac{r(a)}{a}\right)^{a-1} \exp \left[ \frac{x}{b} \right] \quad (5)$$

In which (a) is the Shape parameter and (b) is the Scale parameter. The best of fit is checked as mentioned above using the Kolmogorov-Smirnov which is defined as follows [1, 11]:

$$D_n = \text{Max} |F_n(y) - F(y)| \quad (6)$$

$$F_n(y) = \frac{\pi(\{i \in \{1, 2, \dots, n\} : y_i \le y\})}{n} \quad (7)$$

$$F(y) = \int_{0}^{y} f(x) dx \quad (8)$$

Where F_n(y) and F(y) are the empirical and theoretical cumulative probability of observing and estimated values respectively?

## 3. MATERIALS AND METHODS

The Loire River is the longest river in France. Its length is about 1013 km and its drain basin is about 117.800 km² (1/5 of the French territory). Mechanical erosion rate is estimated to be ca 10 t km⁻² year⁻¹. It's
input of water to the Atlantic Ocean is 26 109 m³ year⁻¹. The solid load ranges from 10⁶ to 4.3 10⁶ t year⁻¹ with the suspended load representing 3% of the total suspended sediment load for rivers draining western Europe. It flows through many major cities, including Orléans which its vale having significant dimensions (300 km², 8 km wide) representing 34% of the total Loire River basin and where this study was conducted [12-17]. TSS and EC were collected from two stations along the path of Loire River. Table 1 shows the UTM Coordinates of these hydrological stations. Figure 1 shows the locations of the hydrological stations along the Loire River. The data was provided by the metrological authorities (Agence de l'eau Loire Bretagne) This data spans twenty years (2001-2021). The first 70% of data was used for building the model (finding the best fitted frequency distribution and its parameters), while the last 30% of data were used for the model verification. The non-parametric Kolmogorov-Smirnov test is used as a test for the goodness of fit.

<table><caption>Table 1: Hydrological station's locations.</caption><thead><tr><th rowspan="2">Station type</th><th rowspan="2">Station name</th><th colspan="2">Coordinates</th><th rowspan="2">Station code</th></tr><tr><th>x</th><th>y</th></tr></thead><tbody><tr><td>Hydrological environmental</td><td>Jargeau</td><td>634435</td><td>6752517</td><td>04050000</td></tr><tr><td>Monitoring</td><td>Meung-Sur-Loire</td><td>602844</td><td>6747759</td><td>04051400</td></tr></tbody></table>

*Projection RGF93 / Lambert 93 (m)

<table><caption>Table 2: Descriptive statistics of the selected stations TSS and EC data along the Loire River (2001-2021).</caption><thead><tr><th rowspan="2">Station name</th><th rowspan="2"></th><th colspan="6">Statistic</th><th rowspan="2">No of Data</th></tr><tr><th>Min</th><th>Max</th><th>Mean</th><th>Std. Deviation</th><th>Skewness</th><th>Kurtosis</th></tr></thead><tbody><tr><td rowspan="2">Jargeau</td><td>TSS</td><td>2.00</td><td>90.00</td><td>19.08</td><td>17.52</td><td>1.90</td><td>4.08</td><td>244</td></tr><tr><td>Ec µS/cm</td><td>166.00</td><td>468.00</td><td>264.34</td><td>38.73</td><td>0.95</td><td>4.49</td><td>242</td></tr><tr><td rowspan="2">Meung-Sur-Loire</td><td>TSS</td><td>2.00</td><td>130.00</td><td>19.76</td><td>19.88</td><td>2.59</td><td>9.35</td><td>258</td></tr><tr><td>Ec µS/cm</td><td>130.00</td><td>517.00</td><td>280.69</td><td>45.14</td><td>0.33</td><td>2.11</td><td>264</td></tr></tbody></table>

<figure><img src="image_5.png" /><figcaption>Figure 1: The locations of the hydrological data measuring stations along the Loire River, France.</figcaption></figure>

## 4. RESULTS AND DISCUSSION

The SIG values of the Kolmogorov-Smirnov test best fit is conducted by using SPSS version 26 software. The acceptance or rejection of null hypothesis is a function of SIG value. The null hypothesis is accepted if it is values more than 0.05 it means that the distribution fits the data otherwise the null hypothesis is rejected accordingly the distribution does not fit the data. Figure 2 shows the best statistical distributions for 70% sub-sample of the data for each station by using the p-p plot. Table 3 shows the SIG test value of the Kolmogorov-Smirnov test and the parameters calculated from fitting the 70% data sub-sample with the 5 mentioned frequency distributions. As shown in Table 4 the best fitted distribution is selected as that of the maximum test SIG value. The TSS parameters in the station MEUNG-SUR-Loire have more than SIG value with the same magnitude. To select the best fit distribution for this station, the t-test for mean and the F-test for variance are used to compare the means and the variances respectively. Table 5 shows the SIG values of the t-test and F
test values. The results can be summarized as follows: the Log Normal (13.71, 0.95) frequency distribution is the best that fits the TSS for the Jargeau station with SIG value of 0.35. For EC of the same station the Weibull (282.911, 8.206) with SIG of 0.877 frequency distribution is selected as the best fit. For Meung-sur-Loire station TSS it is noted there are two distributions that have the same Kolomogrove-smirnov SIG values, the Weibull and the Exponential, the Weibull distribution (19.49, 1.18) is selected with SIG value of 0.75. The Weibull 299.40, 7.50 distributions with value of SIG of 0.99 is the best fit for this station for EC.

<figure><img src="image_6.png" /><figcaption>Figure 2: Fitting of best statistical distribution by using P-P plots for the selected stations.</figcaption></figure>
<table><caption>Table 3: The test statistic (SIG) of Kolmogorov-Smirnov test and the estimated parameters of five statical distributions for the two stations, 70% data sub-samples.</caption><thead><tr><th rowspan="2">Distribution</th><th rowspan="2">Parameters</th><th colspan="2">LOIRE À JARGEAU</th><th colspan="2">LOIRE a MEUNG-SUR-L</th></tr><tr><th>TSS</th><th>EC</th><th>TSS</th><th>EC</th></tr></thead><tbody><tr><td rowspan="3">Normal</td><td>μ</td><td>20.42</td><td>266.77</td><td>19.29</td><td>281.11</td></tr><tr><td>σ</td><td>18.36</td><td>40.69</td><td>20.49</td><td>45.55</td></tr><tr><td>SIG</td><td>0.00</td><td>0.25</td><td>0.00</td><td>0.59</td></tr><tr><td rowspan="3">Log Normal</td><td>μ</td><td>13.71</td><td>263.83</td><td>12.18</td><td>277.40</td></tr><tr><td>σ</td><td>0.95</td><td>0.14</td><td>0.99</td><td>0.16</td></tr><tr><td>SIG</td><td>0.35</td><td>0.80</td><td>0.09</td><td>0.68</td></tr><tr><td rowspan="3">Weibull</td><td>a</td><td>21.33</td><td>282.91</td><td>19.49</td><td>299.40</td></tr><tr><td>b</td><td>1.26</td><td>8.20</td><td>1.18</td><td>7.50</td></tr><tr><td>SIG</td><td>0.22</td><td>0.87</td><td>0.75</td><td>0.99</td></tr><tr><td rowspan="3">Exponential</td><td>μ</td><td>0.11</td><td>0.00</td><td>0.05</td><td>0.00</td></tr><tr><td>SIG</td><td>0.22</td><td>0.0E0</td><td>0.75</td><td>0.0E0</td></tr><tr><td>a</td><td>1.23</td><td>42.97</td><td>0.88</td><td>38.07</td></tr><tr><td rowspan="3">Gamma</td><td>a</td><td>0.06</td><td>0.16</td><td>0.04</td><td>0.13</td></tr><tr><td>b</td><td>0.22</td><td>0.25</td><td>0.18</td><td>0.76</td></tr><tr><td>SIG</td><td>0.22</td><td>0.25</td><td>0.18</td><td>0.76</td></tr></tbody></table>

<table><caption>Table 4: The test statistic (SIG) of Kolmogorov-Smirnov for comparison of the observed (70% of data sub-sample) and a three generated series for each of TSS and EC of the two stations.</caption><thead><tr><th rowspan="2">Distribution</th><th rowspan="2">Generated Series No</th><th colspan="2">LOIRE À JARGEAU</th><th colspan="2">MEUNG-SUR-LOIRE</th></tr><tr><th>TSS</th><th>EC</th><th>TSS</th><th>EC</th></tr></thead><tbody><tr><td rowspan="3">Normal</td><td>1</td><td></td><td></td><td></td><td></td></tr><tr><td>2</td><td></td><td></td><td></td><td></td></tr><tr><td>3</td><td></td><td></td><td></td><td></td></tr><tr><td rowspan="3">Log Normal</td><td>1</td><td>0.53</td><td></td><td></td><td></td></tr><tr><td>2</td><td>0.10</td><td></td><td></td><td></td></tr><tr><td>3</td><td>0.66</td><td></td><td></td><td></td></tr><tr><td rowspan="3">Weibull</td><td>1</td><td></td><td>0.07</td><td>0.13</td><td>0.27</td></tr><tr><td>2</td><td></td><td>0.04</td><td>0.49</td><td>0.37</td></tr><tr><td>3</td><td></td><td>0.16</td><td>0.76</td><td>0.89</td></tr><tr><td rowspan="3">Exponential</td><td>1</td><td></td><td></td><td>0.01</td><td></td></tr><tr><td>2</td><td></td><td></td><td>0.01</td><td></td></tr><tr><td>3</td><td></td><td></td><td>0.03</td><td></td></tr><tr><td rowspan="3">Gamma</td><td>1</td><td></td><td></td><td></td><td></td></tr><tr><td>2</td><td></td><td></td><td></td><td></td></tr><tr><td>3</td><td></td><td></td><td></td><td></td></tr></tbody></table>

<table><caption>Table 5: Results of the t and F - test values for checking the difference in means and variances of the observed series with the generated series for the (30% of data sub-sample), for TSS and EC of the two stations.</caption><thead><tr><th rowspan="3">Distribution</th><th rowspan="3">Series No</th><th colspan="2">LOIRE À JARGEAU</th><th colspan="2">LOIRE À JARGEAU</th><th colspan="2">MEUNG-SUR-LOIRE</th><th colspan="2">MEUNG-SUR-LOIRE</th></tr><tr><th colspan="2">TSS</th><th colspan="2">EC</th><th colspan="2">TSS</th><th colspan="2">EC</th></tr><tr><th>T-Test</th><th>F-Test</th><th>T-Test</th><th>F-Test</th><th>T-Test</th><th>F-Test</th><th>T-Test</th><th>F-Test</th></tr></thead><tbody><tr><td rowspan="3">Normal</td><td>1</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>2</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>3</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td rowspan="3">Log Normal</td><td>1</td><td>0.32</td><td>0.47</td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>2</td><td>0.18</td><td>0.02</td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>3</td><td>0.15</td><td>0.05</td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td rowspan="3">Weibull</td><td>1</td><td></td><td></td><td>0.79</td><td>0.15</td><td>0.08</td><td>0.16</td><td>0.20</td><td>0.42</td></tr><tr><td>2</td><td></td><td></td><td>0.92</td><td>0.00</td><td>0.14</td><td>0.01</td><td>0.53</td><td>0.65</td></tr><tr><td>3</td><td></td><td></td><td>0.52</td><td>0.15</td><td>0.50</td><td>0.48</td><td>0.31</td><td>0.56</td></tr><tr><td rowspan="3">Exponential</td><td>1</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>2</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>3</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td rowspan="3">Gamma</td><td>1</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>2</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>3</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr></tbody></table>

The obtained parameters of the five frequency distributions and the strategy of selecting the best one for each station is dependent on the 70% sub-sample data. To verify the selection of the best frequency distribution, three generated series are obtained using the best fit distribution and is compared with the 30% of the data which are not utilized in obtaining the best fit frequency distribution. Table 4 shows all the values
of SIG for the three generated series using Kolmogorov-Smirnov independent two samples test. It is observed the values of SIG for the three generated series for the TTS and EC for the two stations are positive and more than 0.05 except for the Exponential distribution for EC of Meung-sur-Loire the values of SIG are negative this confirm that the Exponential distribution doesn't fit the data of EC so the other SIG values of the Weibull distribution is adopted for The EC for this station. The positive values of SIG which more than >0.05 confirm the applicability to generate the concentration of the EC for this station which have the same frequency distribution of observed ones. Table 6 shows the frequency of occurrence of TSS exceedance over specified threshold values for the observed and three sets of generated data obtained using the best fit distribution for each of the stations. Comparing the frequency of occurrence of exceeding threshold values assigned in the table between the observed of 30% of data and the generated series shows excellent performance for the two stations. Similar results are observed for the EC as shown in Table 7. This confirms that the obtained frequency models for TSS and EC for these two stations can be used for forecasting, hydrological and other related studies. In addition, they provide a good reference for decision makers and planners for future projects for related events such as floods and/or droughts. Furthermore, Knowledge of the pattern of extreme concentrations will be beneficial in many disciplines such as the agriculture, environment, building projects and construction.

<table><caption>Table 6: Comparison of frequency of occurrence of TSS between observed and the three generated series of the two stations for 30% of data.</caption><thead><tr><th>Station name</th><th>Series</th><th>Lower</th><th>Upper</th><th>FQ P&lt;=50</th><th>FQ P&lt;=100</th><th>FQ P&lt;=150</th></tr></thead><tbody><tr><td rowspan="4">LOIRE à JARGEAU</td><td>Observed</td><td>2</td><td>89</td><td>1.0</td><td>0.0</td><td>0.0</td></tr><tr><td>Generated1</td><td>2</td><td>129.56</td><td>0.9</td><td>0.1</td><td>0.0</td></tr><tr><td>Generated2</td><td>1.34</td><td>119.54</td><td>0.9</td><td>0.1</td><td>0.0</td></tr><tr><td>Generated3</td><td>2</td><td>159.75</td><td>0.9</td><td>0.1</td><td>0.0</td></tr><tr><td rowspan="4">MEUNG-SUR-LOIRE</td><td>Observed</td><td>2</td><td>110</td><td>0.9</td><td>0.1</td><td>0.0</td></tr><tr><td>Generated1</td><td>0.2</td><td>110</td><td>1.0</td><td>0.0</td><td>0.0</td></tr><tr><td>Generated2</td><td>0.52</td><td>110</td><td>1.0</td><td>0.0</td><td>0.0</td></tr><tr><td>Generated3</td><td>0.32</td><td>110</td><td>1.0</td><td>0.0</td><td>0.0</td></tr></tbody></table>

<table><caption>Table 7: Comparison of frequency of occurrence of EC between observed and the three generated series of the two stations for 30% of data.</caption><thead><tr><th>Station name</th><th>Series</th><th>Lower</th><th>Upper</th><th>FQ P&lt;=100</th><th>FQ P&lt;=200</th><th>FQ P&lt;=300</th><th>FQ P&lt;=400</th></tr></thead><tbody><tr><td rowspan="4">LOIRE à JARGEAU</td><td>Observed</td><td>185.00</td><td>326.00</td><td>0.0</td><td>0.0</td><td>0.9</td><td>0.1</td></tr><tr><td>Generated1</td><td>164.67</td><td>330.74</td><td>0.0</td><td>0.1</td><td>0.8</td><td>0.2</td></tr><tr><td>Generated2</td><td>142.46</td><td>336.62</td><td>0.0</td><td>0.0</td><td>0.8</td><td>0.2</td></tr><tr><td>Generated3</td><td>174.74</td><td>326.94</td><td>0.0</td><td>0.1</td><td>0.7</td><td>0.2</td></tr><tr><td rowspan="4">MEUNG-SUR-LOIRE</td><td>Observed</td><td>192.00</td><td>366.00</td><td>0.0</td><td>0.0</td><td>0.6</td><td>0.4</td></tr><tr><td>Generated1</td><td>4192.00</td><td>366.00</td><td>0.0</td><td>0.0</td><td>0.7</td><td>0.3</td></tr><tr><td>Generated2</td><td>166.97</td><td>368.59</td><td>0.0</td><td>0.0</td><td>0.5</td><td>0.4</td></tr><tr><td>Generated3</td><td>141.49</td><td>366.00</td><td>0.0</td><td>0.1</td><td>0.6</td><td>0.3</td></tr></tbody></table>

## 5. CONCLUSIONS

The TSS and EC data of each of two stations Jargeau and Meung-sur-Loire are analyzed and modeled. The results of the analyses show the following conclusion.

* The average values of TSS and EC in the station Meung-sur-Loire is more than those in the station Jargeau. This increase is reasonable as the second station is located about 40 km downstream of the location of the first one along the Loire River. Along this reach there are so many disposals' outfalls of storm water and treated sewage water that will increase the concentration of these two parameters.

* For Meung-sur-Loire metrological station it was found that more than one frequency distribution can fit the TSS with the same degree of fitness the Weibull and exponential distributions. However, it is found that the series generated by the exponential distribution had a small SIG value for Kolmogorov-Smirnov test when compared with the observed data so the other distribution is selected to best fit the data.

* The results can be summarized as follows: the Log Normal (13.71, 0.95) frequency distribution is the best that fits the TSS for the Jargeau station with SIG value of 0.35. For EC of the same station the Weibull (282.911, 8.206) with SIG of 0.877 frequency distribution is selected as the best fit. Meung-sur-Loire station is noted there are two distributions that have the same SIG values for the TSS the Weibull and Exponential, the Weibull distribution (19.49, 1.18) is selected with SIG value of 0.75 the Exponential distribution with SIG value is rejected by the Kolmogorov-Smirnov test.
test to generate. The Weibull 299.40, 7.50 distributions with value of SIG of 0.99 is the best fit for this station for EC.

* The observed best fit distributions found for each of the stations for the electrical conductivity and the TSS using a 70% sub-sample of the data, were validated by comparing the probabilities of different thresholds obtained from three generated series using the obtained model, with the observed 30% data sub-sample that is not contributed in the model development. The observed probabilities match well the generated ones.

## ACKNOWLEDGEMENT

We would like to express our deep gratefulness to "Agence De L'eau Loire-Bretagne France," for providing the data especially Mr.Jean-Baptiste Chatelain. Great appreciation for Prof. Dr. Rafea Al Suhili Professor (Full) at City College of New York for the valuable information.

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