Forecasting Shrimp and Fish Catch in Chilika Lake over Time Series Analysis

Chilika lagoon (a Ramsar site) is a large source of fish production and biodiversity situated in the east coast of India, Odisha. Shrimp landings contribute an average of 4185 MT (Metric Ton) around 35% of total fish production. In this study, SARIMA (Seasonal Auto Regressive Integrated Moving Average) model has been developed on quarterly time series shrimp catch data during the year 2001 – 2015 and forecasted up to 2018. The best model was selected on Akaike Information Criteria (AIC) and Bayesian Information Criterion (SBC). Results showed that maximum average shrimp landings were observed in the first quarter period (sum-mer season), whereas maximum variation in catch was observed during second quarter Q2 (monsoon season) and lowest variation in the fourth quarter Q4 (winter season) catch during the year 2001 – 2015. The developed time series SARIMA (0,1,1)(0,1,1) 4 model was found to be the best fitted model for the shrimp landings in the lagoon. This article also delineates the application of SARIMAX model (SARIMA with regressors) using monthly catch prediction of fisheries in the Chilika Lake. The developed model is validated with less than 10% errors showing increasing fish catch in the upcoming years by maintaining the present lake condition.


Introduction
Coastal lagoon is a junction of fresh, brackish, and marine water system and known for its large fish species production and diversity among aquatic ecosystem [1,2]. The fresh and saline water combination makes it more liable for attracting different finfish and shellfish species in the aquatic ecosystem. The Chilika lake (lagoon) (a Ramsar site of International importance) is the largest brackish water lagoon in the eastern coast of India situated between latitude 19°20 0 13.06″-19°5 4 0 47.02″ N to longitude 85°06 0 49.15″-85°35 0 32.87″ E in the humid tropical climatic zone in the state of Odisha, India ( Figure 1). The lagoon is composed of fresh, brackish and marine water ecosystems and divided into outer channel, central sector, northern sector and southern sector. The lagoon is a rich source of fisheries production and biodiversity, which harbours more than 29 species of shrimp from 8 families [3], providing livelihood around 0.2 million people around it. Fisheries resources in Chilika lake account more than 71% total valuation of the lake ecosystem [4]. The lake has been supporting around 200 million rupees to the state economy and contributing to the earning of valuable foreign exchange. However, continued natural changes and unabated anthropogenic pressure fisheries suffered the most in terms of both yield and biodiversity in the last two decades [5]. Before restoration (opening of the new lake mouth, year 2000-2001) of the lagoon, the Penaeid prawns' population decreases due to the failure in breeding as the lake mouth was shifted far (about 30 Km) from the lake proper, and the confluence point of outer channel (recruitment route) at Magarmukh was silt-choked [5]. Average fisheries catch increased around 520% after four years of new lake mouth opening in 2000. Northern sector was found to have maximum catch percentage of total catch followed by central sector, southern sector and outer channel. The commercial fish catch of the lagoon is composed of 12 fish groups namely mullets, clupeoides, perches, threadfins, crockers, beloniformes, catfishes, tripod fishes, cichlids, murrels, featherbacks and others. After the opening of new lake mouth and desiltation of outer channel, the salinity of the lake increases due to high intake of sea water, resulting favourable for effective recruitment of all economic fishes except cichlids. Shrimp production individually contributed 35% of total fish production in the Chilika lagoon. Some dominating shrimps are To support the prediction of shrimp catch landing in the lagoon, domain specialists need to develop the forecasting models over time series analysis. Time series data are a sequence of data which are collected at successive equally spaced time interval, and it depends on its past value. Time series analysis built stochastic models based on time correlations of collected data. The main objective of time series analysis in respect to the fishery fields is to describe the underlying structure using input data to provide short-term Map of Chilika lagoon (lake) consisting four ecological sectors (outer channel, central sector, northern sector and southern sector) (Source: [14]).
forecasts of the output variables of a dynamic system [6]. Very well-known Box Jenkin's [7] Auto Regressive Integrated Moving Average (ARIMA) model is used to analyse and forecast the univariate time series data. SARIMA model is composed of ARIMA model including seasonal component of the time series data and very frequently used for time series modelling. Applications of ARIMA and SARIMA models were used to analyse and forecast fisheries data [12][13][14]; illustration on catch and effort data for the skipjack tuna fleet at Hawaii [8], Saila [9] modelled on monthly average catch per day of rock lobster, Sathianandan and Srinath [10] modelled of all India marine fish landings using ARIMA model, while NunoPrista et al. [11] described the application of SARIMA models for data-poor fisheries with a case study on sciaenid fishery of Portugal. Modelling and forecasting of marine fish production in Odisha, India, using the SARIMA Model [12].
When exogenous variable is included in the ARIMA model, it is known as ARIMAX model. Similarly, SARIMAX model is developed using well-known seasonal ARIMA model with external regressors associated with the time series data. SARIMAX model performs with better accuracy in fish catch prediction than the SARIMA model with minimum error variance [14]. However, the environmental factors' influence as a regressor in the time series ARIMA (SARIMA) model could be quantified by identifying the underlying patterns in periodic time series data using ARIMAX (SARIMAX) model. The influence of water quality parameters of Chilika lake on monthly catch of commercial fisheries (Beloniformes: order) and total fisheries of the lake was modelled using SARIMAX modelling approach [13,14]. In this case study, SARIMA model for modelling and forecasting the 15 years quarterly time series shrimp catch data of Chilika lagoon of post restoration period since 2001 was developed as case study and further using this model to forecast shrimp catch landings up to 2018. Very few studies have been conducted based on time series model based forecasting of fish species in general and shrimp in particular of Chilika lagoon. The aim of this study is to develop the best fitted time series forecasting model for shrimp landing in Chilika lagoon and further model based catch forecast up to the period 2018. Since catch prediction in advance would be necessary for appropriate planning and designing of the national fishery development plan for sustainable exploitation of fisheries of the said water bodies, this shrimp forecasting study in the Chilika lagoon will be immensely useful in decision making for the policy makers and lagoon managers for sustainable fisheries production and management. In this chapter, a case study of shrimp prediction model using quarterly time series data of the Chilika lagoon was developed, and further prediction model of fisheries and commercial fish (Beloniformes: order) in the Chilika lagoon was also discussed.

Study area
Chilika Lagoon ( Figure 1) water spread area fluctuates between monsoon and dry season at maximum of 1165 km 2 to minimum of 906 km 2 , respectively [15,16]. The water quality of lagoon is influenced by the influx of sea water from West Bengal, Mahanadi distributaries and from the western catchment rivers. The lagoon is an assemblage of shallow to very shallow marine, brackish and freshwater ecosystems [15] characterised by the lagoon with marine, brackish and freshwater fisheries. Shrimp landing plays a significant contributor in commercial landings after the opening of new lagoon mouth as a part of hydrological intervention for eco-restoration of the lake in September 2000.

Sample data collection
The quarter wise estimated total shrimp catch (MT) data and monthly total fish catch (MT) data along with physicochemical parameters of water quality [14] of the Chilika lagoon for the period April 2001 to March 2015 were collected from Chilika Development Authority (CDA). The systematic random sampling methods with landing centre approach [17][18][19] modified with site-specific conditions followed on monthly basis were used to catch estimation in Chilika lagoon. In this study, quarter wise (seasons) catch of the shrimp was taken; such as first quarter (Q1) consists of March, April and May months together (summer season); second quarter (Q2) consists of June, July and August months (monsoon season); third quarter (Q3) consists of September, October and November months (post monsoon season) and fourth quarter (Q4) consists of December, January and February months (winter season). This quarter wise shrimp catch and total fish catch data for the period 2001 to 2015 of the Chilika lagoon were used for the development of SARIMA time series prediction modelling, and SARIMAX model has been described using monthly total fish catch data with the physicochemical parameters of water quality of the lagoon [14].

Resource distribution mapping
Annual shrimp catch distribution mapping at 5-year interval is presented using ArcGIS version 9 software.

SARIMA and SARIMAX model development
ARIMA model is developed on stationary data, but very few data sets in the fisheries field are found to be stationary in nature. It becomes mandatory to test the time series data sets for stationarity before using for modelling. Augmented Dickey-Fuller [20,21] (ADF) test used to test stationary of the original time series data. If data were found to be nonstationary, then it is made stationary by transformation procedure. Stationary time series data were further used for SARIMA model development. SARIMA model was developed by Box-Jenkins [7] Seasonal Auto Regressive Integrated Moving Average (SARIMA) model for seasonal quarterly time series data following four steps as model identification, parameter estimation and model validation (diagnostic checking) and finally forecasting by the following methodology: SARIMA model defined as ARIMA with seasonal parameters denoted as ARIMA (p,d,q) (P,D,Q) s, where p = auto regression (AR) order, d = differencing order, q = moving average order, P = seasonal AR order, D = seasonal differencing order, Q = seasonal MA order and s is seasonality using the back shift operator B (the operator B is such that where, Parameters of the model are ϕ 1 , ⋯, ϕ p , θ 1 , ⋯, θ q , φ 1 , ⋯, φ P , Θ 1 , ⋯, Θ Q and σ 2 . Now, SARIMA model for time series data y t using Eq. (1) can be defined as; Moreover, the SARIMAX model (seasonal ARIMA with explanatory variable) can be represented as a time-series forecasting model using the multiple regressions with seasonal ARIMA model that takes care of the residual's serial correlations.
Further, SARIMAX model can be defined using Eq.
(2) and regressors as follows; Where, x t is the input series at time t and β is the regression coefficients of the input series considering the assumptions of ARIMA and regression model together [22].
Here, the sequence ε 0 t S is independently and identically distributed (i.i.d) random variable with zero mean and constant variance σ 2 , which represents the error term in the model.
Model parameters estimation and its significance were performed using statistical software such as SAS, R, MATLAB, SPSS, etc. Generally 70% data sets were taken for model development and 30% data for model validation for long time series data, but one can change the percentage based on the data availability. Model development approach (a) model identification: model parameters are identified by investigating autocorrelation function (ACF) and partial auto correlation function (PACF) of the time series data (see [23] for more details); (b) parameter estimation: identified model parameters are estimated using various recursive statistical algorithms computation [23]; (c) model validation: inspection of residuals for no significant lags using ACF. The best model was selected based on model selection criteria and finally forecast is done data using best model for the given period of time. The known model selection criteria (minimum is better), such as Akaike [24], known as Akaike Information criterion (AIC), Bayesian Information Criterion proposed by Schwartz [25], known as SBC and R square fit statistics, RMSE (root mean square error), are used for identification of the best fitted model. The minimum is preferable criteria except R square (maximum) for identifying best selection model. Finally, the Ljung and Box [26] statistics Q based on the autocorrelations of the residuals were used for testing adequacy of estimated models. Finally, forecasting or prediction for the short term period is done based on best fitted model. For shrimp catch forecasting modelling, Quarter wise shrimp catch data for the period April, 2001 to March, 2013 was used for best model selection and estimation and the data April, 2014 and March, 2015 were used for validation of the model for Chilika lagoon. Further based on developed model, quarterly shrimp catch was forecasted up to 2018. Further SARIMAX model is described using monthly total fish catch data with the physicochemical parameters of water quality as a factor of regressor of the lagoon as regressors [14]. The total fish data sets for the period April 2001--March 2011 were used for training data sets, and the period April 2011-March 2014 was used as testing and validation data sets for the model.

Results
The quarter wise shrimp catch landings (total, mean and standard deviation) of Chilika lagoon are shown in  15) are found to be more than Q2 (468.91), but the variation in catch in Q2 (164.69) is higher than Q1 (126.61). The mean catch of Q3 (214.41) is similar to that of Q4 (215.10), but the variation in catch in Q3 (84.03) is higher than Q4 (55.60). The variation in quarter wise shrimp catch data in Chilika lagoon was shown in Figure 2. Temporal variation using image mapping of the lagoon in Figure 3 showed that catch increases in the first decade but decreases thereafter, and in 2015, catch was found comparatively low with respect to 2010-2012. The highest peak in catch was observed during 2011 and then starts decreasing till 2015 ( Figure 3).
The best fitted SARIMA model was selected based on model selection criteria (AIC and SBC), and SARIMA (0,1,1)(0,1,1) 4 model with lowest AIC (509.23) and SBC (517. 26) found the best fitted model Table 2. The parameter's estimate of bestfitted SARIMA (0,1,1)(0,1,1) 4 Table 3 showed nonseasonal moving average (component) parameter Q at lag 1 (0.71, p < 0.001) and seasonal moving average parameter (0.78, p < 0.001) at lag 4 as significant effect in the developed model. Two catches of second quarter for the year 2005 and 2011 showed the significant outliers, and catch showed significantly increase during this period. The R 2 value 0.70 showed the good fit of the SARIMA (0,1,1)(0,1,1) 4 model. The residual of the developed SARIMA model was tested by Ljung, and Box test (p > 0.05) showed the adequacy of the fitting of the estimated models. The developed SARIMA model was validated with the actual shrimp catch data ( Table 4). The annual catch prediction error for the developed model was found below 10%,      Table 4). The quarter wise forecast of shrimp catch for the period 2016-2018 with 95% upper and lower catch was shown in Table 5. The quarter wise actual catch versus predicted catch with 95% confidence limit of shrimp catch for the period of 2001 to 2018, showing an increase in catch with respect to 2015, is shown in Figure 4.

model in
An application of SARIMAX model for total fish production forecasting is analysed for Chilika lagoon [14]. Mullets, clupeids, engraulids, perches, catfishes, sciaenids, threadfins, cichlids, tripod fishes, featherbacks, murrels, carps and     1,0,0)(2,0,0)12 was found to be the best fitted model. Here, SARIMA (1,0,0)(2,0,0)12 model is also compared with the SARIMAX (1,0,0) (2,0,0)12 (SARIMA (1,0,0)(2,0,0)12 with regressors as factor) and found that the R square value is greater for SARIMAX than SARIMA and root mean square error is less for SARIMAX than the SARIMA model, which reveals that SARIMAX model is better performer than the SARIMA model for the forecasting of the total fish catch of the lagoon. The regressor, i.e., temperature and salinity used for SARIMAX development, showed significantly positive influence (p < 0.05) on the fish catch in the lagoon. Using SARIMAX model, forecasting is done for the fish production within the error catch less than 10% (for details please see [14]; Figure 5). Total fish catch forecasting also showed an increasing catch in the upcoming year till 2018 with respect to the base year 2015.

Discussion
In Chilika lagoon, fisheries in general and shrimp catch in particular play an important role in support of livelihoods of fishermen around it. The quarterly catch variation in shrimp landings in lagoon could be due to direct or indirect influence by hydrology and environmental condition of the lagoon system [27][28][29]. Average shrimp landings during first quarter Q1 were maximum, which reflects the summer season (March, April and May) catch and the lowest in third quarter Q3 representing the post-monsoon season (September, October and November). The maximum variation in shrimp catch was observed during second quarter Q2 representing monsoon season and lowest variation in fourth quarter Q4 winter season (December, January and February). Seasonal and environmental variation influences the special trends of fisheries in the estuaries system [30]. Physicochemical parameters such as salinity and water temperature influence the distribution of various Penaeid shrimp [31]. The physicochemical parameters of the Chilika lagoon are very much influenced by the seasonal variation as it is connected with the fresh water river by one side and the Bay of Bengal on the other side. The fresh water flow showed positive, negative and inconsistent influence on fish production in the coastal lagoon system for different fish species across different countries [32]. The major commercial fishes in the lake are mostly migrant species (between sea and lake) and account more than 86% of the total fish diversity [33]. For feeding and breeding purpose, the migrant species enter the lake from the sea. The lagoon environment becomes favourable in post winter through summer due to the more availability of food. The higher temperature and salinity phase triggers spawning activity of many clupeid species which contribute more than 26% of total annual catch. Hence, in general, more number of fish species abundance is influenced by the temperature and salinity of the lagoon. As reported, the total fish production showed an increase trend in catch with the increase in temperature and salinity [14]. Similar observation was made as marine-dependent species increased from February month to onset of monsoon (June) [19] in Chilika lagoon. Moreover, during monsoon season, the nutrient inflow in the lake comes through catchment runoff and fresh water, which induces plankton production during post winter and summer (high salinity and temperature) period.
The information on fisheries catch prediction in advance plays a crucial role for managing fisheries resources in the lagoon ecosystem. In fisheries, several time series models were developed and forecasted for fisheries catch data such as ARIMA model, multiple linear regression, non-linear regression and dynamic models, Gaussian autoregressive model, etc. [34][35][36], but in general, ARIMA models have been widely used for better forecasting. SARIMA model is found good fit for short time series catch data and used as common forecasting model by several researchers [34,37,38]. This study also analysed and forecast the quarterly shrimp landing of Chilika lagoon using SARIMA time series modelling approach using data for the period 2001-2015. The best fitted SARIMA (0,1,1)(0,1,1) 4 model developed for the shrimp catch in Chilika lagoon was validated with actual quarterly catch data for the period 2014-2015 and further quarter wise forecast of the shrimp catch up to the year 2018. The forecast of shrimp catch for the years 2016, 2017, and 2018 shows an increase in catch by 4.5, 5.9, and 7.36% with respect to the base year 2015 if the environmental condition of the lagoon remains the same. SARIMAX (1,0,0)(2,0,0) 12 also showed the total fish increasing catch up to year 2018 with respect to the base year 2015. These model-based fish catch forecasting for Chilika lagoon results will be useful for understanding fish catch forecast with acceptable accuracy that will enable lagoon fish managers to facilitate fisheries management by predicting the lagoon fisheries progress toward fish production. Reliable fish catch production forecasting methods are important for managers for confident decision making in fishery management. Hence, the study suggests the regular monitoring and maintenance of fish catch and water quality data to be continued for assessing fisheries trends to enable corrective steps for short-and long-term management interventions in the lagoon.

Conclusions and future work
Time series SARIMA (0,1,1)(0,1,1) 4 model and SARIMAX (1,0,0)(2,0,0)12 model are statistical forecasting models for predicting time series quarterly catch of shrimp production and monthly total fish production in Chilika lagoon. Seasons play a significant influence in shrimp and total fish production in the lagoon. Model prediction showed shrimp and total fish catch of the lagoon will increase in the upcoming years by maintaining the present environmental and ecological conditions of the lagoon. Summer and monsoon seasons have explicit influence on shrimp production in the lagoon. Salinity and temperature of the lagoon positively influence on the total fish catch in the lagoon. Model predicts that shrimp and total fish catch will increase in the upcoming years till 2018 with respect to the base year 2015 in the lagoon. Therefore, continuous monitoring in the lagoon is essential to manage its rich and productive fishery resources, as well as its ecological integrity. This information would provide kind support to the managers of Chilika Development Authority to continue the present efforts for getting a good rich production for the livelihood of the fishermen dependent upon and sustainable management of fisheries. This time series model based study will be useful for forecasting fish production in different lagoon or aquatic system. Besides the catch and water quality monitoring, some related information regarding average monthly influx of tides in respect of amplitude and duration may be recorded for correlation with the catch variability of important species and consideration in trend analysis.
Kolkata, India, for providing laboratory facilities and other logistics for completion of this research work.