### 1. Introduction

##### (1)

$$\begin{array}{l}Chlor-a-2={[10]}^{(0.2830-2.752x+1.457{x}^{2}+0.659{x}^{3}-1.403{x}^{4})}\\ x=\text{log\hspace{0.17em}}[\text{max\hspace{0.17em}}[{R}_{rs}(488)/{R}_{rs}(551).{R}_{rs}(443)/{R}_{rs}(551)]]\end{array}$$*R*

*(λ): represents the remote sensing reflectivity of wavelength λ.*

_{rs}##### (2)

$$\begin{array}{c}Chlor-a-3={[10]}^{(0.289-3.20x+1.2{x}^{2})}\\ x=\text{log\hspace{0.17em}}[{R}_{rs}(488)/{R}_{rs}(551)]\end{array}$$### 2. Data

### 2.1. Field Data

##### Table 1

### 2.2. Satellite Data

### 3. Method

^{2}) are defined by the relationships in Eq. (3), (4) and (5), respectively.

##### (5)

$${R}^{2}=\frac{{\sum}_{i=1}^{n}\left({C}_{i}^{n}-\frac{1}{N}{\sum}_{i=1}^{n}{C}_{i}^{n}\right)({C}_{i}^{m}-\frac{1}{N}{\sum}_{i=1}^{n}{C}_{i}^{m})}{\sqrt{{\sum}_{i=1}^{n}{\left({C}_{i}^{n}-\frac{1}{N}{\sum}_{i=1}^{n}{C}_{i}^{n}\right)}^{2}{{\sum}_{i=1}^{n}\left({C}_{i}^{m}-\frac{1}{N}{\sum}_{i=1}^{n}{C}_{i}^{m}\right)}^{2}}}$$### 4. Results and Discussion

### 4.1. Implementation and Evaluation of Empirical Algorithms

### 4.2. Implementation and Evaluation of Artificial NNs

#### 4.2.1. Neural network with one hidden layer

^{2}, however, was, which is relatively low and indicates a low correlation between the actual and expected network outputs.

#### 4.2.2. Neural network with two hidden layers

^{2}) is higher for the two-layer network, though. Generally, in NNs with two hidden layers, the average R

^{2}is about 0.5 (unacceptable for model efficiency) – i.e., there is a higher correlation with the expected responses than for a single-layer network, with an average R

^{2}of about 0.36.

#### 4.2.3. Evaluation of the effect of training sample numbers

### 5. Concluding Remarks

The experimental algorithms used do not make useful estimates of chlorophyll-A concentrations in coastal areas of the Caspian Sea. Chlor-a-2 and Chlor-a-3 resulted RMSE = 0.47 μg/L and RMSE = 0.79 μg/L, respectively – i.e., Chlor-a-3 was better but their precision are inadequate after all.

In networks with one hidden layer, the network with 15 neurons is most accurate and in networks with two hidden layers (5, 5) neurons is the best. Both the single and two hidden layer networks achieved RMSEs of about 0.1 μg/L under good conditions. As the accuracy of the field data used to train the networks was also about 0.1 μg/L, it is clear that both types of NN are suitable for use estimating chlorophyll-A concentrations in the Caspian Sea from MODIS sensor data.

considering the value of 0.5 / lit for chlorophyll-A, the relative tolerance of the neural network response, which is obtained by dividing RMSE = 0.1 by 0.5, is estimated to be about 20%. In other words, the accuracy of this network can be 80%. Due to the relative accuracy of field observations in the same range, this is the highest expectation that we can use the neural network to estimate the chlorophyll-A content in terms of training data. Comparison of the single- and two-layer NNs shows that, while their accuracies are almost the same, the mean value of R

^{2}in the two-layer network is the better of the two. Single-layer networks are slightly better than those with two layers, however. On the other hand, the network with two layers needed less training (fewer samples) than the single-layer one, to achieve about 0.1 μg/L precision, matching the training samples’ accuracy.The study showed that the optimal NN for estimating chlorophyll-A concentrations from MODIS images in Caspian Sea coastal areas is one with two hidden, 5 neuron layers. It has an RMSE of 0.064 μg/L with a correlation coefficient of about 50% in the best situations.