Manuscript_w_Appendices.rmd

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title: 'Improving landings forecasts using environmental covariates: a case study on the Indian oil sardine (*Sardinella longiceps*)'
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*data version SardineForecast `r packageVersion("SardineForecast")`* (accepted paper used 1.11)

Elizabeth Eli Holmes$^1$, Smitha BR$^2$, Kumar Nimit$^3$, Sourav Maity$^3$, David M. Checkley, Jr.$^4$, Mark L. Wells$^5$, Vera L. Trainer$^1$

1\. Northwest Fisheries Science Center, National Marine Fisheries
Service, NOAA, Seattle, WA, USA.

2\. Centre for Marine Living Resources and Ecology, Ministry of Earth
Sciences, Kochi, India.

3\. Indian National Centre for Ocean Information Services, Ministry of
Earth Sciences, Hyderabad, India.

4\. Scripps Institution of Oceanography, University of California San
Diego, CA, USA.

5\. School of Marine Sciences, University of Maine, Orono, ME, USA.

**Corresponding author**: Elizabeth Eli Holmes, PhD. Northwest Fisheries
Science Center, 2725 Montlake Blvd E, Seattle, WA 98112 USA,
+1-206-419-6164, eli.holmes\@noaa.gov

**Running title**: Improving landings forecasts with covariates

**Keywords:** Indian oil sardine, catch prediction, GAM modeling,
dynamic linear modeling, climate, sea surface temperature, remote
sensing, Southeast Arabian Sea, Multidecadal Oscillation

**Author Contributions:** All authors were involved in the
conceptualization and writing -- review and editing. Individual authors
had these additional roles. Elizabeth Holmes: Data curation,
methodology, formal analysis, software, and writing -- original draft.
Smitha BR: Writing -- original draft. Kumar Nimit: Data curation and
writing -- original draft. Sourav Maity: Visualization. David Checkley
and Mark Wells: Methodology, writing -- revisions and review. Vera
Trainer: Funding acquisition and project supervision.

**ACKNOWLEDGEMENTS**

We thank the U.S. National Marine Fisheries Service and the Indian
Ministry of Earth Sciences for support of the joint U.S.-Indian research
project: "Collaboration on the Development of a Fisheries and Harmful
Algal Bloom and Monitoring and Prediction System in Indian Seas" which
jointly provided the financial support for the research visits. The
visits took place at the Indian National Centre for Ocean Information
Services (INCOIS) and Centre for Marine Living Resources and Ecology
(CMLRE). We thank these institutes for their support. We would like to
specifically thank Dr. Usha Varanasi (University of Washington) for her
vision, knowledge and perseverance in conceptualizing, initiating and
sustaining this important fisheries science collaboration between the
governments of India and the USA. We would also like to acknowledge the
support of Dr. S.S.C Shenoi (INCOIS), Dr. M. Sudhakar (CMLRE), Dr. N.
Saravanane (CMRLE), Dr. Ned Cyr, and Ed Gorecki (NOAA). The sardine
landings data have been collected and analyzed by the Central Marine
Fisheries Research Institute (Kochi, India) since the 1950s; we
acknowledge the many researchers involved in collecting and maintaining
this long-term data set. We also thank the many INCOIS, CMLRE, and CMFRI
scientists who participated in the research visits and who helped us
understand the biology, fishery and fishery data and gave input into the
analyses.

# ABSTRACT

Commercial landings of sardines are known to show strong year-to-year
fluctuations. A key driver is thought to be environmental variability,
to which small forage fish are especially sensitive. We examined the
utility of including environmental covariates in forecasts for landings
of the Indian oil sardine using a long-term time series of quarterly
catches. Potentially influential variables examined included
precipitation, upwelling intensity, sea surface temperature (SST), and
chlorophyll-a concentration. All of these have been shown to be
important for oil sardine growth and survival, spawning and/or movement
into the nearshore fishing regions. However, improving out-of-sample
landings forecasts using environmental covariates has often proven
elusive. We tested the inclusion of environmental covariates in forecast
models using generalized additive models, which allow for non-linear
responses, and dynamic linear models, which allow for time-varying
responses. Only two environmental covariates improved out-of-sample
prediction: the 2.5-year average regional SST and precipitation over
land during June-July. The most significant improvement was with the SST
covariate and post-monsoon landings with a 19-22% reduction in
mean-squared prediction error. Models with the second best covariate,
monsoon precipitation over land, provided a 4-8% reduction in prediction
error. We also tested large-scale ocean climate teleconnection indices.
One, an index of the Atlantic Multidecadal Oscillation, also improved
out-of-sample predictions similarly to the multiyear average regional
SST. The earth's changing climate is associated with both rapid warming
in the Western Indian Ocean and changes to monsoon rainfall patterns.
Our work highlights these as key variables that can improve forecasting
of oil sardine landings.

# 1 INTRODUCTION

Environmental variability is known to be a key driver of population
variability for small forage fish, such as sardine, anchovy, and herring
(Alheit & Hagen, 1997; Checkley, Asch, & Rykaczewski, 2017; Cury et al.,
2000). In particular, ocean temperature and upwelling dynamics have been
shown to substantially affect the recruitment success and biomass of
European and Pacific sardines (*Sardina pilchardus* and *Sardinops
sagax*, respectively; Alheit et al., 2012; Garza-Gil, Varela-Lafuente,
Caballero-Míguez, & Torralba-Cano, 2015; Jacobson & MacCall, 1995;
Lindegren & Checkley, 2012; Lindegren, Checkley, Rouyer, MacCall, &
Stenseth, 2013; Rykaczewski & Checkley, 2008). The Indian oil sardine
(*Sardinella longiceps* Valenciennes, 1847) is among the most
commercially important fish resources along the southwestern coast of
India---historically comprising up to 20% of the total marine fish
landings in India (Vivekanandan, Srinath, Pillai, Immanuel, & Kurup,
2003). Similar to landings of other sardines, oil sardine landings show
strong interannual fluctuations with larger decadal booms and busts, but
Indian oil sardine landings also have an unusually strong seasonal cycle
driven by the summer monsoon. Landings peak in October--December, after
the summer monsoon, and reach a nadir in April--June.

Two environmental variables, precipitation and coastal upwelling
intensity, have been the focus of much research on the effect of the
ocean environment on Indian oil sardine life history and landings.
Precipitation during the summer monsoon and the day of monsoon arrival
are thought to act as direct or indirect cues for spawning (Antony Raja,
1969, 1974; Jayaprakash, 2002; Murty & Edelman, 1966; Pitchaikani &
Lipton, 2012; Srinath, 1998; Xu & Boyce, 2009). At the same time,
intense monsoon rain over land causes high nutrient flux from rivers
into the shallow nearshore regions which causes eutrophication and
anoxia (Chauhan et al., 2011). The strong seasonal upwelling along the
southwestern coast of India is also thought to be a key driver of
variability in oil sardine abundance and catches. Coastal upwelling
during the summer monsoon has dual effects: it fuels productivity but at
high levels brings low oxygen water to the surface which can cause fish
to move offshore where they are inaccessible to the fishery, while
downwelling during spring is thought to promote the spring migration of
adults into the nearshore where they are exposed to the fishery (Hamza,
Valsala, Mallissery, & George, 2020). Correlations have been identified
between landings and various indices of upwelling intensity (Hamza et
al., 2020; Jayaprakash, 2002; Kripa et al., 2015; Longhurst & Wooster,
1990; Madhupratap, Shetye, Nair, & Nair, 1994; Murty & Edelman, 1966;
Srinath, 1998; Thara, 2011); direct measures of upwelling-associated
productivity (George et al., 2012; Madhupratap et al., 1994; Manjusha,
Jayasankar, Remya, Ambrose, & Vivekanandan, 2013; Menon et al., 2019;
Nair, 1952; Nair & Subrahmanyan, 1955; Piontkovski, Al Oufi, & Al
Jufaily, 2014; Pitchaikani & Lipton, 2012); and the cold nearshore sea
surface temperatures caused by upwelling (Annigeri, 1969; Pillai, 1991;
Prabhu & Dhulkhed, 1970; Supraba et al., 2016).

In addition, to these regional environmental variables, climate
teleconnection indices which capture large-scale ocean modes have also
been examined for association with fisheries landings. Large-scale ocean
climate modes, such as the El Niño--Southern Oscillation (ENSO), Indian
Ocean Dipole (IOD) and Atlantic Multidecadal Oscillation (AMO), have
cascading effects on a variety of ocean conditions that affect small
pelagics (Alheit & Hagen, 1997; Alheit et al., 2019; Bakun, Roy, &
Lluch-Cota, 2008; Schwartzlose et al., 2010). Correlations have been
found between ocean climate indices and oil sardine landings (Hamza et
al., 2020; Rohit et al., 2018; Supraba et al., 2016), as well as with
coastal anoxic events (Vallivattathillam et al., 2017) and chlorophyll
blooms (Currie et al., 2013) in our study region.

This long and rich history of research on the Indian oil sardine
provides a strong foundation for selecting and specifying the
environmental factors that are most likely affecting the abundance and
catchability of this important commercial species. In this paper, we
study the utility of using these environmental covariates to improve
out-of-sample landings predictions for the oil sardine, with the
ultimate goal of improving short-term operational forecasts.

## 1.1 Modeling and forecasting fishery landings

The modeling and forecasting of landings using time-series models has a
long history in fisheries research (Cohen & Stone, 1987; Farmer &
Froeschke, 2015; Georgakarakos, Doutsoubas, & Valavanis, 2006; Hanson,
Vaughan, & Narayan, 2006; Lawer, 2016; Lloret, Lleonart, & Sole, 2000;
Mendelssohn, 1981; Nobel & Sathianandan, 1991; Prista, Diawara, Costa, &
Jones, 2011; Stergiou & Christou, 1996), including for oil sardines
(Sajna et al., 2019; Srinath, 1998; Venugopalan & Srinath, 1998). These
models can be used to identify variables correlated with catch
fluctuations and to provide short-term landings forecasts, which are
useful for fishery managers (e.g., Farmer & Froeschke, 2015) and the
fishing industry (e.g., Hanson et al., 2006; Schaaf, Sykes, & Chapoton,
1975).

One of the interesting puzzles in research on landings forecasting, and
forecasting in general, is that it is often difficult to improve on
simple low-dimensional autoregressive forecast models, that is a
forecast that is a simple function of past values (Ward, Holmes,
Thorson, & Collen, 2014), and adding environmental covariates often
degrades the forecast due to the added parameter estimation costs. The
Indian oil sardine offers a unique opportunity to study the utility of
environmental covariates for landings forecasts because there is
extensive prior research of the environmental variables that influence
the oil sardine's ocean environment and its exposure to the fishery and
there is a long-term quarterly catch time series derived from a
large-scale stratified statistical survey beginning in the 1950s
(Srinath, Kuriakose, & Mini, 2005).

We first developed an autoregressive base catch model using only the
prior year landings to explain the current year landings. Environmental
covariates were then added to the base model and we examined whether the
covariate decreased the out-of-sample prediction errors and explained
catch variability beyond that explained by the base model. We tested
models with linear, non-linear and time-varying covariate effects. We
focused primarily on covariates derived from remote sensing products due
to their broad spatial availability and temporal resolution, which make
them practical for future operational forecasting efforts. The
covariates were selected based on prior research supporting their
correlation with nearshore productivity, juvenile growth and survival,
and movement into or out of the nearshore (where they are exposed to the
fishery); see Table 1.

## 1.2 Study area

The study area is located off the Kerala coast of India (Figure 1 and
2), where the majority of Indian oil sardines are landed and where this
species comprises about 40% of the marine fish catch (Srinath, 1998;
Vivekanandan et al., 2003). It is in the Southeast Arabian Sea, one of
the world's important seasonal upwelling zones (Habeebrehman et al.,
2008; Madhupratap, Gopalakrishnan, Haridas, & Nair, 2001). The portion
of the study area falling between 9$^{\circ}$N$\text{\ and}$
13$^{\circ}$N has especially intense upwelling in June--September due to
the combined effects of wind stress (Figure 2) and remote forcing (BR,
2010; BR, Sanjeevan, Vimalkumar, & Revichandran, 2008; Shah et al.,
2019). Upwelling gives rise to a strong temperature differential between
the nearshore and offshore, and high primary productivity and surface
chlorophyll (BR, 2010; Chauhan et al., 2011; Habeebrehman et al., 2008;
Shafeeque et al., 2019). Primary productivity subsides after September,
whereas mesozooplankton abundances increase and remain high in the
post-monsoon period (Madhupratap et al., 2001).

## 1.3 Oil sardine life cycle and fishery interaction

The Indian oil sardine fishery is restricted to the narrow strip of the
western Indian continental shelf, \<20 km offshore (Figure 1; Rohit et
al., 2018). The yearly cycle begins with spawning in June and July,
corresponding to the onset of the summer monsoon (Antony Raja, 1969) and
much lower nearshore SSTs due to upwelling (Figure 3). Mature fish
migrate from offshore to spawning areas (Antony Raja, 1964), and
spawning begins when temperature, salinity, and food availability are
conducive to larval survival (Jayaprakash & Pillai, 2000; Krishnakumar
et al., 2008; Murty & Edelman, 1966; Nair, Joseph, Kripa, Remya, &
Pillai, 2016). After an initial peak, spawning continues into September
(Antony Raja, 1969; Hornell, 1910; Hornell & Nayudu, 1924; Prabhu &
Dhulkhed, 1970). Both early- and late-spawning cohorts are evident in
the length distributions of fish in the fall catch. After spawning,
adults migrate closer to the coast (Figure 1), where the spent fish
become exposed to the fishery and landings begin to increase. Catches
during summer are dominated by these 1--2.5-year-old mature fish (Antony
Raja, 1969; Bensam, 1964; Nair et al., 2016).

Spawned sardine eggs develop rapidly into larvae (Nair, 1959). The
phytoplankton bloom that provides food for the larvae depends on
nutrient influx from coastal upwelling and runoff from rivers during the
summer and early fall (Shafeeque et al., 2019). Blooms start near the
southern tip of India in June, then increase in intensity and expand
northward with the peak of bloom intensity remaining south of
13$^{\circ}$N, the northern end of Kerala (BR, 2010). Variation in the
bloom initiation time and intensity leads to changes in the food supply,
and thus in larval growth and survival and subsequent recruitment of
0-year sardines into the fishery (George et al., 2012). Oil sardines
grow rapidly in the first few months of life, and spikes of 0-year fish
from early spawning appear in the August and September catches in most
years (Antony Raja, 1970; Nair et al., 2016). During late summer and
fall, both adult and juvenile sardines shoal and feed in the nearshore
following the intense plankton blooms that develop off the Kerala coast.
Oil sardines remain inshore to feed through winter and peak catches
occur in October-December followed by January-March (Figure 4). These
post-monsoon, October--March, catches are mixed age including fish from
0--2 years (Antony Raja, 1970; Nair et al., 2016; Prabhu & Dhulkhed,
1970; Rohit et al., 2018). In March--May, the sardines move offshore to
deeper water where they are no longer available to the fishery, landings
consequently decline (Figure 4), and the seasonal cycle begins anew.

Landings are products of abundance, effort and catchability (i.e.,
availability to the nearshore fishery). For much of the period of our
study, the Indian oil sardine fishery was largely unregulated and has
been a nearshore fishery dominated by small boats. For this time period,
the yearly landings are often assumed to reflect total abundance for
species- and fishery-specific reasons (cf. Kripa et al., 2018). The ring
seine was introduced in this fishery in the 1980s (Das & Edwin, 2018),
but widespread mechanization of the fleet is a recent development.
Fishers with small boats with no refrigeration have limited ability to
target stock, at least not to the degree that landings would remain
constant as abundance declines, as can be seen with a large, mobile,
highly mechanized fleet. The fishery is unregulated, except for a brief
closure during the summer monsoon, and thus landings are not affected by
area closures or catch limits. Finally, the fishery is dispersed along
the entire coastline, rather than being focused from a few large ports.
Thus, the relationship between landings and abundance can be assumed to
be strong for our data set and comparison of the landings to the
available catch-per-unit effort (hours fishing) data shows high
correlation (Hamza et al., 2020). Seasonal variation in the oil sardine
catch is affected both by movement of fish in and out of the nearshore
(Figure 1) and recruitment of juvenile fish to the fishery.

# 2 MATERIALS AND METHODS

## 2.1 Sardine landing data

The Central Marine Fisheries Research Institute (CMFRI), Kochi, India,
has collected quarterly fish landing data along the country's
southwestern coast since the early 1950s using a stratified multistage
sampling design which accounts for the different boat and gear types
(Srinath et al., 2005). We used CMFRI data from the Indian state of
Kerala (Figure 1), which has the longest and most complete time series
and where the overwhelming majority of oil sardines are landed (Figure
4). Quarterly oil sardine landings data (in metric tons) for all gear
types used in Kerala were obtained from CMFRI reports (1956--1984) and
online databases (1985--2015). See the Supplemental Information: Data
sources and raw data. These data were log transformed to stabilize
variance and to facilitate additive modeling.

## 2.2 Environmental data

We analyzed monthly composites of SST, chlorophyll-a concentration,
precipitation, upwelling indices derived from SST and winds, and ocean
climate indices (Figures 2 and 5). For each covariate, specific months
(seasons) were used corresponding to different aspects of oil sardine
life-history and its interaction with the nearshore fishery. These are
summarized in Table 1. See the Supporting Information: Data sources and
raw data for all environmental data details, sources and code to compute
metrics and download the data.

We tested SST (°C) averaged between 8° and 13°N in the nearshore (within
1° of the coast) in June-September (summer monsoon period of peak
upwelling, spawning, larval growth and survival) and October-December
(peak juvenile somatic growth). SST in the current year could affect
landings by causing fish movement in and out of nearshore and/or
affecting juvenile abundance while prior year effects would arise via
effects on cohort strength. We tested SST regionally, between 8° and
13°N and up to 2° off-shore, in the spring (March-May) and over the
prior 30 months (January *t-2* to June *t*). The former may affect egg
development, spawning and inshore migration timing thus affecting both
current and future year abundance and availability to the fishery. The
latter integrates effects of SST over the average sardine lifespan and
has been shown to be correlated with recruitment in other sardine
species (Checkley et al., 2017). For our SST source, we used the Daily
Optimum Interpolation (OI), Version 2.1 data set by the Group for High
Resolution Sea Surface Temperature (GHRSST). This data set uses Advanced
Very-High Resolution Radiometer (AVHRR) data, which provides accurate
nearshore SST values, and interpolates to fill in gaps in the AVHRR
data. See the section on comparison of SST products in the Supplemental
Information: Full model tests and diagnostics. We used OI SST for all
the main analyses which use landings data after 1981. For our analysis
of the effect of the regional- (as opposed to nearshore-) SST prior to
1981, we used the International Comprehensive Ocean-Atmosphere Data Set
(ICOADS) SST product, available from 1960. The nearshore (\<80km) ICOADS
SST measurements are not as accurate as AVHRR and could not be used for
our covariates involving nearshore SST, such as the nearshore-offshore
SST differential.

The strength of upwelling during the summer monsoon June to September
has been widely studied for its effects on coastal productivity and
coastal anoxia. The upwelling dynamics in our study area are unusual in
that remote oceanographic forcing is an especially important driver of
the seasonal upwelling intensity in combination with forces from local
wind stress (BR, 2010; BR et al., 2008; Rao, Joshi, & Ravichandran,
2008). We used a variety of SST- and wind-based indices that have been
used in recent papers on upwelling dynamics off the southwest coast of
India. We tested both current year effects which could arise via effects
on abundance or lower catchability due to movement offshore to avoid
nearshore anoxia and prior year effects which would arise via cohort
strength in the prior year. The first index was the SST differential
between nearshore and 3° longitude offshore, based on Naidu, Kumar, and
Babu (1999) and BR et al. (2008). This index has a strong temporal
association with chlorophyll-a blooms (Figure 3) and is able to measure
upwelling arising due to both remote-forcing and local wind stress. SSTs
were obtained from the AVHRR remote-sensing data set described above.
The second index was the Ekman Mass Transport (EMT; kg m^-1^ s^-1^)
perpendicular to and within 2° longitude of the coast (Schwing,
O\'Farrell, Steger, & Baltz, 1996; Shafeeque et al., 2019). The third
index was the Ekman Pumping (W~e~; m s^-1^) at the tip of India (Shah et
al., 2018). EMT and W~e~ are computed from surface winds and capture
upwelling due to local wind-stress. We used the Reanalysis Data ERA5
monthly 10m winds from the European Centre for Medium-Range Weather
Forecasts. See the Supplemental Information: Ekman Mass Transport and
Pumping Calculations for the equations and code for computing EMT and
W~e~ from surface winds and for a comparison of the ERA5 winds to other
remote-sensing wind products.

Precipitation over land and over the ocean during the summer monsoon
(June to September) and spring (April to May) were tested in both the
current and prior year. Precipitation over land leads to river
discharge, which has various and large influences, positive and
negative, on the nearshore ocean environment. Precipitation data were
obtained from two sources: monthly precipitation (in millimeters) over
Kerala, obtained with land-based rain gauges and available from the
Indian Institute of Tropical Meteorology from 1956; and daily
precipitation (averaged monthly) over the ocean from remote-sensing (via
the NOAA Global Precipitation Climatology Project). From the latter, we
extracted data for the 2.5° × 2.5° box defined by latitude 8.75--11.25°N
and longitude 73.25--75.75°E off the Kerala coast. The land and
nearshore ocean precipitation data are correlated (Supporting
Information; Figure S6).

Satellite-derived chlorophyll-a data are only available since September
1997 and were not the focus of our analysis due to low sample size,
however, were included for preliminary study. We examined current and
prior year effects of chlorophyll-a in the summer monsoon (June to
September) period of peak upwelling and peak blooms (Figure 3) and in
the October to December period of peak juvenile somatic growth. For
chlorophyll-a concentration (mg m^-3^), we used the R2018.0 and R2018.1
products developed by the NASA Ocean Biology Processing Group of the
Ocean Ecology Laboratory.

We used four climate indices that have been found to correlate with
either oil sardine landings, coastal anoxia, chlorophyll-a, or upwelling
intensity in recent studies: Oceanic Niño Index (ONI), the Dipole Mode
Index (DMI), the Pacific Decadal Oscillation (PDO) index, and the
Atlantic Multidecadal Oscillation (AMO) index. The ONI is a measure of
the SST anomaly in the east-central Pacific and a standard index of the
ENSO cycle. The DMI is defined by the SST anomaly difference between the
western and southeastern Indian Ocean and is an index for the Indian
Ocean Dipole cycle. It has been shown to predict anoxic events in our
study area (Vallivattathillam et al., 2017) and seasonal chlorophyll-a
blooms in the southeastern Indian Ocean (Currie et al., 2013). The PDO
and AMO indices are measures of the SST anomalies in the North Pacific
and North Atlantic Oceans, respectively. Hamza et al. (2020) found
significant correlation between PDO and AMO indices and multiyear
fluctuations in oil sardine landings. For ONI, PDO and AMO indices, we
created an annual covariate from the average July *t-1* to June *t*
values. The yearly average was computed this way so that it would not
overlap with the July-September catch that we are forecasting.

## 2.3 Base catch models

The first step in our analysis was to determine our base models for
current catch as a function of past catch. We modeled July--September
(late-monsoon) and October--March (post-monsoon) catches separately, for
biological and statistical reasons. Unlike the October--March catch, the
July--September catch contains mainly mature spawning-age fish, is
affected by the monsoon fishery closure, and is affected by the timing
of post-spawning movement inshore which exposes fish to the fishery. The
covariates that affect the timing of spawning and post-spawning inshore
movement may differ from those that affect egg, larval and juvenile
survival, and nearshore shoaling (and thus the size of the October-March
catch). Separating the catches into seasons, and analyzing annual
series, eliminated the confounding influence of seasonality and
permitted a focus on year-to-year variability rather than the seasonal
cycle. Although adults in July-September would be those that spawn the
0-year fish in the October-March catch, the July-September catch in year
*t* was not used as a predictor for October-March catch in year *t*. The
focus of our work is the study of forecasting performance; the
July-September catch numbers would not be available by October (the
quarter immediately after).

We found little support for autoregressive errors, i.e., Autoregressive
Integrated Moving Average (ARIMA) models with moving average (MA)
components, based on diagnostic tests of the residuals and model
selection. The best-supported ARIMA models were simple AR models
($x_{t} = \alpha + bx_{t - 1} + \epsilon_{t}$) where the error-term
$\epsilon_{t}$ was temporally independent. Similar lack of strong
autocorrelation in residuals has been found in other studies using ARIMA
catch models for small pelagics (Stergiou & Christou, 1996). We thus
used AR-only models; however, we tested linear and non-linear models
with generalized additive models (GAMs; Wood, 2017) of the form
$x_{t} = \alpha + s\left( x_{t - 1} \right) + \epsilon_{t},$ where *s*(
) is a non-linear spline smoothing function, and time-varying linear
models with dynamic linear models (DLMs) of the form
$x_{t} = \alpha_{t} + b_{t}x_{t - 1} + \epsilon_{t}$. GAMs enable
modeling of the effect of a covariate as a flexible non-linear function,
and DLMs allow the effect of the covariate to vary over time. Our GAM
approach is analogous to that taken by Jacobson and MacCall (1995) in a
study of the effects of SST on Pacific sardine recruitment.

We explored four classes of base catch models: a naïve (null) model,
linear regressive models with 1--2 years of prior catch data, DLMs
(using the MARSS package in R; Holmes, Ward, & Wills, 2012), and GAMs
(using the mgcv package in R; Wood, 2011). We fit GAMs with smooth terms
represented by penalized thin-plate regression splines and fixed the
smoothing term at an intermediate value (sp = 0.6) to obtain smooth
responses, as multimodal or overly flexible response curves would not be
realistic for our application. The catch models were:

-   naïve (null): $ln(C_{i,t}) = ln(C_{j,t - 1}) + \epsilon_{t}$
-   biased random walk:
    $ln(C_{i,t}) = \alpha + ln(C_{j,t - 1}) + \epsilon_{t}$
-   linear AR-1:
    $ln(C_{i,t}) = \alpha + \beta ln(C_{j,t - 1}) + \epsilon_{t}$
-   linear AR-2:
    $ln(C_{i,t}) = \alpha + \beta_{1}ln(C_{j,t - 1}) + \beta_{2}ln(C_{k,t - 2}) + \epsilon_{t}$
-   DLM AR-1:
    $ln(C_{i,t}) = \alpha_{t} + \beta_{t}ln(C_{j,t - 1}) + \epsilon_{t}$
-   GAM AR-1: $ln(C_{i,t}) = \alpha + s(ln(C_{j,t - 1})) + \epsilon_{t}$
-   GAM AR-2:
    $ln(C_{i,t}) = \alpha + s_{1}(ln(C_{j,t - 1})) + s_{2}(ln(C_{k,t - 2})) + \epsilon_{t},$

$\ \ln\left( C_{i,t} \right),\ ln\left( C_{j,t - 1} \right),\ ln(C_{k,t - 2})$
are the log catches. *t*, *t-1* and *t-2* denote current, prior year and
two years prior. *i*, *j* and *k* denote the season: July-September
(denoted *S* for late-summer) or October-March (denoted *W* for winter)
catch depending on the model.

We tested models with October--March $(W_{t - 1}$ and $W_{t - 2}$), and
July--September ($S_{t - 1}$ and $S_{t - 2}$) catches 1 and 2 prior
years as the explanatory catch variables (the $C_{j,t - 1}$ and
$C_{k,t - 2}$). $S_{t}$ was not used as a predictor for $W_{t}$ because
$\text{it}$ is the immediately preceding quarter.

The catch models were fit to 1983--2015 catch data, the time-period for
which our SST, upwelling, and precipitation data were available for all
years; we used the same years of catch data for all covariate tests.
Akaike information criterion corrected for small sample size (AICc) and
leave-one-out cross-validation (LOOCV) were applied to nested sets of
models to evaluate model support. LOOCV involves model fitting with the
omission of a data point, followed by prediction of that data point. The
root mean squared error (RMSE) and median absolute error (MdAE) are
reported for the set of LOOCV prediction errors. After selection of the
best model using the 1983--2015 data, fitting was repeated with catch
data from 1956--1982 to confirm the base catch model. An influential
years test was performed by removing each year in the series
sequentially and repeating the model selection analysis (Supporting
Information: Validation of catch base models, Figures S1-S5).

## 2.4 Covariate analysis

Once the base catch models were determined, the environmental covariates
(Section 2.2) were studied. The covariate models were selected to test
specific hypothesized drivers of catch variability based on how and when
environmental variables are thought to affect oil sardine survival and
recruitment and to affect availability to the fishery (summarized in
Table 1 and Section 2.2). As with the catch models, support was
evaluated using AICc and LOOCV with nested sets of models. The full sets
of nested models are shown in the appendices (Tables A1 and A2) and
Supplement Table S7. Models with covariates (*V*) with linear and
non-linear (GAM) effects were compared:
$ln(C_{i,t}) = M + \alpha + \beta_{1}V_{t} + \epsilon_{t}$ and
$ln(C_{i,t}) = M + \alpha + s(V_{t}) + \epsilon_{t}$, where $M$ is the
best catch model from the preliminary model fitting step described
above. The smoothing term for the GAM models was fixed at an
intermediate value (sp = 0.6). Note, in all cases, prior catch was the
most important variable; that is, the environmental covariates were
never more important than prior catch in terms of explaining variance.

Research has suggested that nutrient input from river discharge is
necessary in order for upwelling to fuel high nearshore productivity
(Shafeeque et al., 2019). To test this, models with a linear or
non-linear upwelling-precipitation interaction were also tested:
$\ln\left( C_{i,t} \right) = M + \alpha + \beta_{1}V_{1,t} + \beta_{2}V_{2,t} + \beta_{3}V_{1,t}V_{2,t} + \epsilon_{t}$
and
$\ln\left( C_{i,t} \right) = M + \alpha + s_{1}\left( V_{1,t} \right) + s_{2}\left( V_{2,t} \right) + ti\left( V_{1,t},V_{2,t} \right){\  + \ \epsilon}_{t},$
where *ti*( ) is a tensor product interaction (non-linear interaction).
Chlorophyll-a was not included in the main analyses since it is only
available since September 1997. Instead, a separate analysis using
1997-2015 data was performed using chlorophyll-a alone as a covariate.
Lastly a DLM covariate model was used to explore models with changing
effects of SST, AMO and precipitation:
$ln(C_{i,t}) = {M + \alpha}_{t} + \beta_{t}V_{t} + \epsilon_{t}$.

All statistical analysis was completed in the R programming language (R
Development Core Team, 2019) using the mcgv (Wood, 2011) and MARSS
(Holmes, Ward, & Wills, 2012) R packages.

# 3 RESULTS

## 3.1 Base catch model selection

For 1983--2015 July--September catches, models with the October--March
catch in the prior year ($ln(W_{t - 1})$) were strongly supported over
the naïve model and over models with the prior-year July--September
catch ($ln(S_{t - 1})$), and models with catch two-years prior
(Tables S1 and S2). Including prior catch with a non-linear response
improved model fit and reduced LOOCV RMSE (Table S2). Three models had
almost identical AICc and LOOCV RMSE (maximum adjusted $R^{2} = 21.7$):
linear and non-linear models with $ln(W_{t - 1})$, and a non-linear
model with $ln(W_{t - 1})$ and $ln(W_{t - 2})$. Similar model selection
results were obtained for the October--March landings (Tables S4 and
S5), but these models explained much more variance (maximum adjusted
$R^{2} = 57.3$). The best-supported model$,$ based on AICc and *F*
values, was the non-linear model with $ln(W_{t - 1})$ and
$ln(S_{t - 2})$ (Tables 2, S4 and S5). The simpler model with only
$ln(W_{t - 1})$ had the second lowest AICc but lowest LOOCV RMSE values.

Repeating the model selection using 1956--1982 data yielded the same
results for the July--September catch, with the non-linear model with
$ln(W_{t - 1})$ having the lowest AICc and LOOCV RMSE values (Table S3).
For the October--March catch, the results were very similar, but not
identical. The non-linear model with $ln(W_{t - 1})$ had the lowest
LOOCV RMSE value, and the models with $ln(W_{t - 1})$ and
$ln(S_{t - 2})$ or $ln(S_{t - 2})$ had the lowest AICs, although the
difference from the AICc for the $ln(W_{t - 1})$ model was \<1 (Table
S6). The DLMs (time-varying effects) performed poorly for the
July--September catch, with high AICc and LOOCV RMSE values. One DLM for
the October--March catch showed mixed performance, with a higher AICc
but lower LOOCV RMSE value. Overall, the model selection indicated that
a catch model with a time-varying effect of prior catch did not improve
either model fit or out-of-sample prediction, but inclusion of a
non-linear effect was important.

We chose the non-linear model with $ln(W_{t - 1})$ as the base catch
model for the July--September catch based on further diagnostic tests
(Supporting Information: Validation of catch base models) and to
minimize the loss of degrees of freedom from an additional covariate,
$ln(W_{t - 2})$.

$M0:ln(S_{t}) = \alpha + s(ln(W_{t - 1})) + \epsilon_{t}$ (adj. *R*^2^ =
21.7)

Two non-linear base models were chosen for the October--March catch:

$M1:ln(W_{t}) = \alpha + s_{1}(ln(W_{t - 1})) + s_{2}(ln(S_{t - 2})) + \epsilon_{t}$
(adj. *R*^2^ = 45.9)

$M2:ln(W_{t}) = \alpha + s(ln(W_{t - 1})) + \epsilon_{t}$ (adj. *R*^2^ =
57.3)

Both models were included as base models for the October--March catch as
one had the best model fit while the other had better out-of-sample
prediction. Both were supported based on the influential years analysis
(Supporting Information; Figures S1-S5).

## 3.2 Environmental covariate selection

The covariate analysis was able to rule out a number of the tested
covariates. Specifically, we found no support for the use of April--May
or June--July precipitation over the ocean, in the current or prior
season or as a linear or non-linear effect, as an explanatory variable
for the July--September or October--March catch (Tables A1, A2, and S7).
We also found no support for the use of March--May (current or prior
year) or October--December SST as an explanatory variable for the
July--September or October--March catch (Tables A1, A2, and S7). In
general, all the indices of upwelling in the current or prior year were
either not or only weakly supported (based on AICc) and did not improve
out-of-sample prediction (LOOCV RMSE or MdAE) (Tables A1, A2, and S7).
The one exception was the July-September catch and the June-September
nearshore SST upwelling index in the current year and Ekman Pumping in
the prior year. These reduced the LOOCV MdAE prediction errors but did
not reduce the LOOCV RMSE errors or AICc for the July-September catch
(Table A1). The Ekman Mass Transport (EMT) upwelling index did not
improve the model fit (AICc) or prediction errors (Table A1 and A2).
Recent research (Shafeeque et al., 2019) suggests that there is an
interaction between upwelling and precipitation, such that both
anomalous precipitation over land and upwelling intensity during the
summer monsoon is needed for strong chlorophyll-a blooms. Our tests
using a variety of interaction models showed that while models with
interactions increased the *R^2^*, the increased parameter cost led to
higher AICc and higher out-of-sample prediction errors (Table A8). Note,
the July-September upwelling indices overlap with the July-September
catch and thus would not be useful for forecasting July-September catch
but were tested to understand the utility of the upwelling indices. We
also found no support for using the ONI or PDO index to improve either
the July--September or October--March catch predictions. The fall DMI in
the prior year reduced AICc and LOOCV RMSE and MdAE but only for
October-March catch with the more complex model (Table 2 and S7).

Only three covariates emerged as explanatory variables that both
explained catch variance (lower AICc) and reduced out-of-sample
predictions errors across models and across different time-periods: the
June-July precipitation over land, the 2.5-year average regional SST,
and the AMO index. The best models included non-linear response curves
(Figure 6). For the July--September catch, the best models had an
adjusted *R*^2^ of 29.9, 47 and 47.5 (precipitation, SST and AMO,
respectively) versus 21.7 for the model without the covariate (Tables 2
and A1), and for the October--March catch, the a$\text{djusted}\ R^{2}$
was 59.6, 65.9 and 63.8 (precipitation, SST and AMO) versus 45.9 using
the simpler base model without covariates and 70.5, 69.5 and 65.6 versus
57.3 with the more complex base model (Tables 2, A2, and S7). These
covariates reduced the median out-of-sample prediction error (LOOCV
MdAE) by up to 19% for the July-September catch and the median and root
mean-squared out-of-sample prediction errors (LOOCV RMSE and MdAE) by up
to 22% for the October-March catch relative to the base model without
environmental covariates (Tables 2, A1, A2, and S7). Figure 7
illustrates the reduction in prediction errors using the 2.5-year
average regional SST as an example (the other covariates are shown in
Figures A1 and A2).

Our examination of the chlorophyll-a covariate was limited, as the
simplest model including the chlorophyll-a concentration required five
degrees of freedom, and catch size varied little in the period for which
we had chlorophyll-a data. The fitting of second-degree polynomial
models to the average log chlorophyll-a concentrations in
July--September and October--December of the current and prior years
yielded no significant result for the July--September catch, but we
found a significant effect of the prior-year October--December
chlorophyll-a concentration on the October--March catch (Tables A1, A2
and S7).

We identified four outlier years in which October--March oil sardine
landings were much lower than predicted based on prior catches: 1986,
1991, 1994, and 2013 (Figure 7c). In the figure, the y-axis is the
predicted catch in a LOOCV analysis thus is the 'left-out' year. The
model with 2.5-year average regional SST predicted the collapses in 1986
and 1991; the predicted catch sizes with this covariate in the model
were much closer to the observed catches (Figure 7d). The 2.5-year
average regional SST did not explain the 1994 collapse, the largest
during the study period, or the 2013 collapse. The same pattern was seen
for the July--September catch, with the exception that this catch was
not unusually low in 1991 (Figure 7a). The 2.5-year average regional SST
reduced the prediction errors for this catch in 1986 but did not
(appreciably) reduce it for 1994 or 2013 (Figure 7b). In fact, no
covariate tested in this study explained the 1994 fishery collapse
(Figures A1 and A2); the prediction error for this year was very high
regardless of any covariate that was included in the model.

## 3.3 Dynamic linear modeling with SST, AMO and precipitation

The ICOADS SST data set does not capture the nearshore SST as accurately
as AVHRR, and thus was not used for our main analyses. Nonetheless the
ICOADS regional SST (as opposed to nearshore) is highly correlated with
the AVHRR regional SST data (Supporting Information; Figure S7), and the
ICOADS SST data extend almost to the start of the catch time series (to
1960). The precipitation data and AMO index also extend to 1960. Using
the dynamic linear model for the October-March catch, we examined
whether the explanatory power (as measured by model residual errors,
i.e., model fit) of these three covariates changed over time.
Time-varying covariate models were fit to the residuals of the simpler
base October-March catch model; the results were very similar with the
more complex October-March catch model thus results using only one of
the October-March base models are shown. The covariates were z-scored
(mean removed and variance standardized to 1) and included as
third-order polynomials to allow a non-linear response. The models took
the form
$r_{t} = \beta_{1,t}V_{t} + {\beta_{2,t}V_{t}^{2} + \beta_{3,t}V_{t}^{3} + \epsilon}_{t}$
where *r* is the catch residual and *V* is the covariate. The *β* were
allowed to evolve as an autoregressive process,
$\beta_{t} = \beta_{t - 1}{+ e}_{t}$, with *e~t\ ~*\~ N(0, *σ*). The *σ*
was chosen such that the model complexity (time-variation) did not
increase out-sample-prediction error over the base catch model (with no
environmental covariates).

The explanatory power of the covariates, even when allowed to be
time-varying and thus flexible enough to fit temporally local
conditions, changed over time. Up to 1990, the land precipitation did
not increase model fit but did afterwards. The 2.5-year average regional
SST and AMO index improved the model fit over the entire time series
(meaning the covariate RMSE line was below that of the model with no
covariates), but especially so from the mid-1980s to late-1990s (Figure
8).

# 4 DISCUSSION

Our results indicate that successful modeling of Indian oil sardine
catch depends on the catch season of interest (monsoon versus
post-monsoon) and selection of the environmental covariate to use in the
model. All the covariates we tested were tied to environmental
conditions known to impact key life-stages of the oil sardine. However
only two regional covariates, the multiyear average regional SST and the
monsoon rainfall over land, and one ocean climate index, the Atlantic
Multidecadal Oscillation index, improved both model fit and
out-of-sample prediction.

## 4.1 Monsoon versus post-monsoon model performance

The July-September catch, which overlaps with the summer monsoon and a
seasonal fishery closure, is difficult to model. The best July-September
models with only prior catch as a covariate explained less than 22% of
the variation while the best model with environmental covariates
explained only 47% of the variation and had median out-of-sample
prediction errors of +/-65% (of raw, not log-transformed, catch). We
found only one covariate that improved the root mean squared
out-of-sample prediction error for the July-September catch (the AMO
index), though a number improved median out-of-sample prediction error.
In contrast, variation in the post-monsoon catch (October-March) was
much better explained. The simpler model with only prior catch as a
covariate explained 45.9% of the variation and the model with the best
covariate, explained 65.9%. The best environmental covariate reduced the
out-of-sample prediction errors (RMSE and MdAE) by ca. 20% and explained
two of the four recent catch collapses.

This result cautions against modeling all quarters of oil sardine catch
together (as one yearly catch). The July--September catch is difficult
to model, as it exhibits high variability that is poorly explained by
past catches or environmental factors. The reasons for this are likely a
combination of variable spawning timing which affects the timing of
movement of adults into the nearshore where they are exposed to the
fishery, the summer monsoon which affects fishing operations, and the
fishery closure during part of this period. In contrast, the
October--March catch, which comprises 60-80% of the catch from July to
June, is much better explained, and its forecasts have smaller
predictive errors. Forecasting all quarters together as a yearly catch
means that the high variability in the July-September catch will hide
the predictability of the subsequent October-March catch.

## 4.2 Sea surface temperature

The SST in October--December, the period of larval and early juvenile
development, may affect survival and growth in multiple ways and thus
correlate with biomass in future years. In some years, extreme heat
events occur in March--May during the period of egg maturation which may
affect spawning and thus the current year and future biomass. However,
we found no correlation of these seasonal SST covariates with the
July--September or October-March catch in the current or future years.

Instead, we found that the regional SST averaged over the prior 2.5
years (January *t-2* to June *t*), corresponding to the lifespan of an
oil sardine, emerged as a consistently informative SST covariate. The
multiyear average regional SST explained variability in the oil sardine
landings and improved out-of-sample catch prediction. Studies conducted
in the California Current System have also found that the multiyear
average SST explains year-to-year variability in Pacific sardine
recruitment (Checkley, Alheit, Oozeki, & Roy, 2009; Checkley et al.,
2017; Jacobson & MacCall, 1995; Lindegren & Checkley, 2013). This
covariate has also been found to correlate with southern African sardine
recruitment (Boyer, Boyer, Fossen, & Kreiner, 2001). McClatchie,
Goericke, Auad, and Hill (2010) found no relationship between SST and
Pacific sardine recruitment; however, they examined this relationship
linearly; in the present study, as in the other cited studies, allowance
of non-linearity in the SST effect was important. Both Jacobson and
MacCall (1995) and Lindegren and Checkley (2013) found a step-like
response function for temperature: below a threshold value the effect of
temperature was linear (and positive) and above the threshold, the
effect was flat (no longer increased). In the linear portion of the
effect curve, the point where the effect curve crosses from negative to
positive represents an important biological threshold. Our analysis
found a similar effect curve with a negative effect when the 2.5-year
average regional SST was below ${28.37}^{\circ}$C and positive above and
with the positive effect leveling off above ${28.5}^{\circ}$C.

The AMO index (July *t-1* to June *t* average) is highly correlated with
the 2.5-year average regional SST covariate used in our analyses
(Pearson correlation ρ=0.70 1983-2016), unlike the other ocean climate
indices: ONI ρ=0.16, PDO index ρ=-0.04 and DMI ρ=0.37 (Supporting
Information; Figure S8). Thus, not surprisingly, the AMO index also
emerged as a consistently informative covariate and provided reductions
in out-of-sample prediction error similar to the multiyear average SST.
None of the other ocean climate indices were informative, except the DMI
but only in the most complex October-March catch model. Teleconnection
between the AMO and the Indian Ocean has been shown in a number of
papers (reviewed in Hu, Hu & Hu, 2018; Zhang et al., 2019). In
particular, there appears to be a relationship between the intensity of
the Indian summer monsoon and the AMO (Lu, Dong & Ding, 2006; Zhang &
Delworth, 2006). The correlation between oil sardine landings and the
AMO index that we (and Hamza et al., 2020) found is likely a reflection
of this large-scale teleconnection that manifests, in part, as
correlation between regional SST and the AMO index.

## 4.3 Precipitation

Since early studies of oil sardines, precipitation during the summer
monsoon has been studied as a variable to explain catch fluctuations
(Antony Raja, 1969, 1974; Murty & Edelman, 1966; Srinath, 1998). While
correlations have been found, the identified correlations between
precipitation and oil sardine landings have been positive in some
studies and negative in others (Madhupratap et al., 1994) and varied
depending on the time period studied. In general, the correlation was
assumed to be positive as rainfall is correlated with monsoon intensity
which is in turn correlated with upwelling and productivity. But heavy
monsoon rain also has negative effects. During heavy rainfall, nutrient
and sediments flow into the nearshore region from rivers, which leads to
short-term eutrophication and anoxia in coastal waters (Chauhan et al.,
2011).

In our study, we compared rainfall over the ocean (using remote-sensing
data) and over the land (using land-gauge data). Though correlated,
these are not identical. We found no correlation between rainfall over
the ocean and catch in any combination of our statistical tests. Oceanic
rainfall was uniformly disinformative---increasing both AICc and
out-of-sample prediction errors---across all combinations of models
tested. In contrast the June-July precipitation over land in the current
season was strongly informative and was the only covariate besides the
multiyear average regional SST and AMO index that improved model fit and
out-of-sample prediction. The effect of precipitation was non-linear;
close to zero for low to moderate rainfall levels and then negative at
high precipitation. This suggests that the negative effect of high
rainfall was the dominant impact. The effects were only seen on the
current year catch and thus may reflect a temporary movement of fish
offshore (away from the fishery) to avoid anoxia rather than a lower
cohort strength that would persist into the next season.

## 4.4 Upwelling

Despite the strong connections of upwelling with productivity which
positively impacts sardine recruitment, growth, and survival, none of
the upwelling indices examined in this study (SST-nearshore-offshore
differential, Ekman Mass Transport, and Ekman Pumping) explained
year-to-year variation in current-year or prior-year landings or
improved out-of-sample forecasts. When we did find a (weak) relationship
with upwelling intensity and catch, the effect was for the current year
only and was negative, rather than positive. The negative effect emerged
at extremely high upwelling. This negative effect is not surprising.
Extremely high upwelling transports larval sardines offshore and brings
to the surface poorly oxygenated water which sardines avoid (Gupta et
al., 2016).

Our tests looked at whether upwelling intensity explained variation and
future catch beyond what could be explained using a catch model with
only prior catch as the covariate. It may be that upwelling affects the
future abundance in a way that is already captured by using prior catch.
Conversely it may be that strong upwelling by itself is not sufficient
for productivity. Shafeeque et al. (2019) looked at the correlation
between summer upwelling strength and precipitation and chlorophyll-a
bloom intensity. They found that chlorophyll-a bloom anomalies were
associated with years with both upwelling and precipitation anomalies,
suggesting an interaction between these two environmental variables.
While we found that models with an upwelling and precipitation
interaction did have higher *R^2^* relative to an upwelling-only or
precipitation-only model, they had higher, sometimes considerably
higher, out-of-sample prediction errors than the base catch model with
no covariates or the base catch model with only precipitation. This
highlights one of the dilemmas of forecasting: increased complexity in a
model often brings a high prediction cost.

The monthly average upwelling metrics we used are those used in many
other studies of upwelling and nearshore productivity in this region. In
most coastal upwelling systems, local wind-stress forces are the most
important driver of upwelling, however the southwest coast of India is
unique in that remote-forcing and local currents and gyres play an
unusually important role in driving the seasonal upwelling intensity
(BR, 2010; BR et al., 2008; Rao et al., 2008; Shah et al., 2019). Our
nearshore-offshore SST differential index should have captured upwelling
intensity due to either wind stress or remote-forcing, and we expected
that it would perform better than the wind-based metrics. However, it
was equally uninformative as a covariate. It may be that other aspects
of upwelling besides average nearshore intensity, such as the timing of
its initiation (e.g., Barth et al., 2007), its spatial extent along the
coast or some metric of daily extreme events are necessary to capture
the conditions relevant to oil sardine landings. We did find support for
a more direct measure of productivity and food availability: the
nearshore surface chlorophyll-a concentration. Chlorophyll-a
concentration in fall, the period of peak juvenile somatic growth,
explained the October-March catch in the next year, reducing
out-of-sample prediction errors by 10% to 20%. With chlorophyll-a data
only available after 1997, the power of our tests was limited, but this
suggests that fall chlorophyll-a concentration, after the summer peak
chlorophyll-a blooms, may prove useful for improving forecasts.

## 4.5 Oil sardine collapses

There were four years when October-March oil sardine landings were much
lower than expected based on prior catches: 1986, 1991, 1994 and 2013.
The 2.5-year average regional SST was able to explain the collapses in
1986 and 1991. The largest collapse was in 1994, when the catch was much
lower than expected even taking into account the prior year declines.
The most recent collapse, in our data set, was 2013. The 2.5-year
average regional SST did not successfully predict the 1994 or 2013
collapses; although the prediction error was reduced for both years, it
was still large. The same pattern was seen for the July-September catch,
with the exception that 1991 was not unusually low. The 2.5-year average
regional SST reduced the prediction error for 1986 but did not
(appreciably) for 1994 nor 2013. In fact, none of the covariates we
tested explained the lower than expected 1994 catch; while only the
precipitation over land in June-July explained the 2013 collapse (but
not 1994, 1991, nor 1986). The 1994 collapse was correlated with severe
nearshore anoxia (Kripa et al., 2015). Since none of the environmental
factors we studied captured the 1994 decline, it suggests that metrics
that more directly measure nearshore anoxia may be necessary.

# 5 CONCLUSIONS

Our study emphasizes a number of key points for developing models for
the purpose of landings forecasting. First, improvements in catch
forecasts beyond what is possible using prior catch (a null
autoregressive catch model) may be elusive. All the environmental
covariates that we tested are closely tied to factors that affect
critical months of spawning, growth, survival and movement of sardines
into the nearshore (where they are exposed to the fishery). Yet almost
none of these explained catch variability, beyond what could be
explained using a simple autoregressive catch model. Second, non-linear
effects are common and important to consider. Third, covariate effects
can change over time. Fisheries exist within complex multi-species
ecological systems and species and their life histories evolve. Forecast
models will need to guard against covariate effects that change over
time and lead to an erosion of forecast performance. Lastly, model
complexity comes at a price particularly when the goal is prediction.
Inclusion of out-of-sample prediction metrics is crucial as these can
give a very different picture compared to metrics for model fit alone.
Covariates that are supported by model fit, even using model selection
metrics that penalize extra complexity, may still be uninformative or
even disinformative for out-of-sample prediction.

Despite all this, we found that there were environmental covariates that
did appreciably improve landings prediction. In particular, the
multiyear average sea surface temperature has now emerged as an
informative covariate across multiple studies on sardine species, and
interestingly, the Atlantic Multidecadal Oscillation index---recently
shown to be correlated to oil sardines landings by Hamza et al.
(2020)---was also an informative covariate in our analysis. This
suggests that the Indian oil sardine is affected by global-scale
processes, in particular the teleconnection between the AMO and Indian
Ocean processes (reviewed in Hu, Hu & Hu, 2018; Zhang et al., 2019). We
see a number of fruitful directions to explore to further improve
short-term forecasts. The first is incorporation of direct leading
indicators of catch. We did not show models with catch in the prior
quarter as a predictor; surveys take time to process and report and thus
data for the immediately prior quarter would not be available. Had we
included the prior quarter catch, the fits and predictions would be much
better. However, models could use preliminary catch numbers from the
beginning of the prior quarter from sentinel landing centers or gear
types. This would be feasible without a new data collection scheme and
would certainly improve the short-term forecasts for the next quarter. A
longer-term approach would be incorporation of recruitment information
from egg or larval density surveys. Such surveys have been conducted on
the U.S. West coast since the 1940s by the California Cooperative
Oceanic Fisheries Investigations (CalCOFI) Program (Gallo et al., 2019),
and these data have been successfully used to improve abundance
estimation and management of the Pacific sardine (McClatchie, 2014).
Leading abundance indicators, such as from preliminary catch data or
larval surveys, are likely to be especially important if climate changes
alter past relationships of catch with the environmental covariates.

The temperature of the Western Indian Ocean has been increasing over the
last century at a greater rate than in any other tropical ocean (Roxy,
Ritika, Terray, & Masson, 2014), and warming has been most extreme
during the summer monsoon months. These changes are affecting the oil
sardine distribution, with significant landings now occurring north of
Goa (Vivekanandan, Rajagopalan, & Pillai, 2009). Continued warming is
expected to affect the productivity of the region via multiple pathways,
including changes in salinity, oxygen concentration, currents, wind
patterns, ocean stratification, and upwelling spatial patterns,
phenology, and intensity (Moustahfid, Marsac, & Grangopadhyay, 2018).
The incorporation of environmental covariates into landings forecasts
has the potential to improve fishery management for small pelagic
species, such as oil sardines, in the face of a changing ocean
environment (Haltuch et al., 2019; Tommasi et al., 2016). However,
careful performance testing of the environmental covariates will be
needed and expectations as to how much environmental covariates can
improve forecasts should be tempered, especially if there are
multi-month lags in the landings data available to include in the
forecast or if new sources of abundance indicators, such as recruitment
surveys, remain unavailable.

# CONFLICT OF INTEREST

The authors have no conflicts of interest to declare.

# DATA AVAILABILITY STATEMENT

The raw data that supports the findings of this study are available in
the data table in the supplementary material of this article. The data
were derived from the following resources available in the public
domain. SST, chlorophyll-a concentration, and ocean currents: NOAA
ERDDAP data server https://coastwatch.pfeg.noaa.gov/erddap. Ocean winds
from the ERA5 Global Reanalysis: Asia-Pacific Data Research Center
ERDDAP data server http://apdrc.soest.hawaii.edu/erddap. Ocean
precipitation: NOAA/NCEI Global Precipitation Climatology Project
https://www.ncei.noaa.gov. Land precipitation: Open Government Data
Platform India https://data.gov.in. ONI: U.S. National Weather Service
Climate Prediction Center https://www.cpc.ncep.noaa.gov. DMI: Japan
Agency for Marine-Earth Science and Technology http://www.jamstec.go.jp.
PDO and AMO: U.S. NOAA Physical Sciences Laboratory
https://psl.noaa.gov/. Landings data: Reports and databases published by
the Central Marine Fisheries Research Institute http://www.cmfri.org.in.

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<!--
# html version has legends with each figure

# FIGURE LEGENDS

**FIGURE 1** The study area, located off the southwestern coast of
India. Kerala is shaded gray.

**FIGURE 2** Seasonal average winds, sea surface temperature (SST) and
currents during the summer monsoon versus the winter non-monsoon months
in the study area. Winds and SST are from the Reanalysis Data ERA5
monthly product and averaged over 1979-2020. The bottom panels show the
main seasonal currents near the study area: the West India Coastal
Current going north in winter and south in summer and the Summer Monsoon
Current going west to east near 8°N.

**FIGURE 3** Key oil sardine life history events (top colored bars),
overlaid on the monthly nearshore and offshore sea surface temperatures
(SSTs; °C) and nearshore chlorophyll-a (Chl-a) concentrations (mg
m^-3^).

**FIGURE 4** Top panel: Quarterly catch data for 1956--2015 from Kerala.
Note that the fishery is closed July 1--mid-August, meaning that the
quarter 3 catch represents only 1.5 months. Mean catches in quarters
1--4 were 38, 19.2, 30.9, and 59.9 metric tons, respectively. Bottom
panel: The seasonal time series (July-September and October-March catch)
used in the paper.

**FIGURE 5** Four of the remote sensing covariates used in the analysis.
All data are monthly averages. The upwelling index was defined as the
difference between the nearshore and 3° longitude offshore sea surface
temperatures (SSTs). Surface chlorophyll-a data are available only from
September 1997 onward. SSTs were obtained from Advanced Very High
Resolution Radiometer (AVHRR) products which provide high resolution
nearshore measurements.

**FIGURE 6** Effect sizes for the 2.5-year average regional sea surface
temperature (SST; within 2° of the Kerala coast), current-season
upwelling intensity (average June-September SST nearshore-offshore
upwelling index off Kochi, Kerala), current season June-July
precipitation over land and the Atlantic Multidecadal Oscillation (AMO)
index in the prior year on July--September and October--March catches.
As the upwelling index reflects the difference between offshore and
nearshore SST, positive values indicate that coastal surface waters are
colder than offshore waters. The more positive the difference, the
stronger the upwelling intensity.

**FIGURE 7** Predicted versus observed catches obtained with models with
and without the 2.5-year average sea surface temperature (SST) included
as a non-linear covariate. The lines indicate a perfect prediction where
observed catch equals the predicted catch. The value to be predicted was
left out in the model fitting. Values above the line are cases where the
prediction was too high and values below the line are cases where the
prediction was too low. a) July--September catch, modeled with only the
prior-season October--March catch as a covariate. b) July--September
catch, modeled with the prior-season October--March catch and 2.5-year
average SST as covariates. c) October--March catch, modeled with the
prior-season October--March catch only. d) October--March, modeled as in
panel c with the addition of the 2.5-year average SST. LOOCV RMSE =
leave one out root mean squared prediction error. See Figures A1 and A2
for the same plots with other environmental covariates.

**FIGURE 8** Model fit over 10-year windows for dynamic linear models of
October-March catch 1960-2015 using the 2.5-year average SST from the
ICOADS data set, June-July precipitation over land (from land gauges),
and Atlantic Multidecadal Oscillation index as covariates. These models
allowed the covariate model to evolve over time. The models were fit to
the residuals of the simpler base model (with only prior October-March
catch as a covariate) with the 1994 residual was removed. The covariates
were z-scored (mean removed and standardized to variance of 1) and
included as a third-order polynomial to allow a non-linear effect. The
plot shows the RMSE of the model residuals computed on a 10-year sliding
window.
-->

# TABLES

```{r child = file.path(here::here(), 'Rmds','Table_1.Rmd')}
```

### &nbsp;

### &nbsp;


```{r child = file.path(here::here(), 'Rmds','Table_2.Rmd')}
```

# FIGURES

```{r child = file.path(here::here(), 'Rmds','Figures.Rmd')}
```

# APPENDICES

```{r child = file.path(here::here(), 'Rmds','Appendices.Rmd')}
```