4.1 ITCZ identification Index

^{Yu and Zhang (2018)} proposed an index to identify the ITCZ second band formation, working with monthly precipitation averaged in three areas (Fig. 3), the northeastern equatorial Pacific (NEP; 180º-85º W, 2º-10º N), the southeastern equatorial Pacific (SEP; 150º-85º W, 10º-2º S), and the eastern equatorial Pacific (EEP; 180º-85º W, 2º S-2º N). In this work, these areas are used to calculate the Yu and Zhang index with monthly and daily satellite estimated precipitation data; also, a new area to identify the formation of the ITCZ second band near the Peruvian coast is proposed. The longitudinal limits of this new area are 91.5º-81.5º W (purple area in Fig. 3), and the same latitudinal limits of NEP, SEP and EEP.

Fig. 3 Areas taken into account for analyzing the ITCZ second band. Yu and Zhang areas (red boxes): NEP (180º-85º W, 2º-10º N), EEP (180º-85º W, 2º S-2º N), SEP (150º-85º W, 10º-2º S). New areas (black boxes): NEPn (91.5º-81.5º W, 2º-10º N), EEPn (91.5º-81.5º W, 2º S-2º N), SEPn (91.5º-81.5º W, 10º-2º S). Purple region is the area considered for temporal wind and precipitation analysis (Fig. 5). 

To show the behavior of the early 2017 rain in the Peruvian western north, we selected eight stations of the National Service of Meteorology and Hydrology (SENAMHI) network distributed in Tumbes and Piura (Figs. 1 and 2).

Daily and monthly estimated precipitation from of TRMM Multi-Satellite Precipitation Analysis (TMPA) January 1 to April 30, with 0.25º of spatial resolution, were used in this work (^{Huffman and Bolvin, 2017}),

For SST and its anomalies (SSTA), data of the Operational Sea Surface Temperature and Sea Ice Analysis (OSTIA) reanalysis was used with a spatial resolution of 0.25º and 1-day temporal resolution (^{Donlon et al., 2012}).

Data from the Era-Interim reanalysis (^{Dee et al., 2011}) was also used with a spatial resolution of 79 km (~0.75º), a temporal resolution of 6 h and 37 pressure levels (from 1000 to 10 hPa). The data used is of 12:00 UTC from January 1 to April 30 2017, while the 1981-2010 period was used for the climatology, as recommended by ^{WMO (2014)}.

For the synoptic analysis, 5-day anomalies of surface winds, sea level pressure, 600 hPa mixing ratio and 200 hPa divergence and winds were considered.

The ITCZ could be identified with analyzes of cloud, precipitation or surface winds (^{Haffke et al., 2016}), and precipitation estimated by TMPA-TRMM, which was used in this paper.

To determine the formation of the ITCZ second band, two indices proposed by ^{Yu and Zhang (2018)} to characterize interannual variability of the eastern Pacific ITCZ during boreal spring (February to April) were used: the asymmetric index (Ia) and double ITCZ index (Id):

where P _NEP is the boreal spring precipitation rate averaged in the NEP, P _SEP is the precipitation averaged in the SEP, P _EEP is the precipitation averaged in EEP, and P _m is the mean precipitation rate in the three regions:

A negative Id index indicates single precipitation maximum at the equator, while positive a Id index indicates double ITCZ. The Ia index distinguishes the preference of the ITCZ to the north (Ia > 0) or south (Ia < 0) of the equator, or a symmetric double ITCZ (Ia = 0).

Using these indices with precipitation between 1979 and 2017, ^{Yu and Zhang (2018)} identified 13 years with maximum precipitation anomalies to the south of the equator: 1984, 1986, 1989, 1996, 1999, 2000, 2001, 2006, 2008, 2009, 2011, 2012, and 2017.

4.2. Lorenz Energy Cycle

The general circulation of the atmosphere may be approximated as a composition of the mean zonal motion and eddies superposed upon it. This allows the division of kinetic (K) and available potential (A) energy of the atmosphere in two types: zonal (Z) and eddy (E). The zonal component of energy surges due to variance of zonally averaged temperature, while the eddy component of energy is associated with the variance of temperature within the latitude circles. Each type of energy is a source or sink of another type (^{Lorenz, 1955}).

Applying the equations of continuity, thermodynamic and motion, and considering transfer of energy across the boundaries in a limited area, ^{Michaelides (1987)} proposed the next equations to express the local variation of A _Z , A _E , K _Z and K _E as:

where Z and E represent zonal and eddy energies, respectively.

According to ^{Lorenz (1967)}, A _Z represents the amount of available potential energy that would exist if the mass field was replaced by its zonal average, and A _E the excess of available potential energy over A _Z . Likewise, K _Z represents the amount of kinetic energy which would exist if the existing zonally averaged motion, but no eddy motion was present, and K _E , the excess of kinetic energy over K _Z .

In Eqs. (4-7), G _Z represents the generation of zonal available potential energy (A _Z ) through the latitudinal differential heating, produced by the diabatic heat sources (^{Asnani, 1993}, ²⁰⁰⁵). G _E represents the generation of eddy potential energy (A _E ) along the same latitude, heating the warm regions and cooling the cold regions, generating gradients of temperature in the same latitude. Physically, the latent heat released due to convection should be an important source of heat and, and consequently of eddy available potential energy (G _E ) (^{Dias, 2010}). C _A (A _Z , A _E ) represents the conversion of the available potential energy between zonal and eddy forms, associated with meridional and vertical gradients of temperature, transporting sensible heat. In physical terms, the zonal averaged temperature in the troposphere decreases toward the poles, and this gradient generates transport of warm tropical air to polar latitudes and cold polar air to warm latitudes through meridional motions. This process decreases the thermal gradient between latitudes, diminishing A _Z , and increases the thermal gradient at the same latitude, resulting in A _E increases, related to wave motion (troughs and ridges) and it is an intermediate process in the baroclinic chain. C _Z (K _Z , A _Z ) indicates the conversion of zonal kinetic energy (K _Z ) into zonal available potential (A _Z ) through upward movements of warm air in low latitudes and downward movements of cold air in high latitudes. According to ^{Asnani (2005)}, the Hadley and Ferrel circulations are manifestations of this conversion. Meanwhile, C _E (A _E , K _E ) represents the conversion of eddy available potential (A _E ) into eddy kinetic energy (K _E ) through upward motions of warm air and downward movements of cold air along the same latitude circle. The equatorial Walker circulation would be a manifestation of this process (^{Aliaga, 2017}). C _K (K _E , K _Z ) represents the conversion of the kinetic energy between eddy and zonal types. According to ^{Lorenz (1967)}, there is no process that converts A _Z into K _E or A _E into K _K . D _K and D _E represent the effects of friction (dissipation) by zonal and eddy motions, respectively. Terms with B represent energy flux across the boundary. All these terms can be expressed in the diagram in Figure 4.

Fig. 4 Diagram of the Lorenz energy cycle (LEC) in a limited area (^{Michaelides, 1987}). Arrows denote the most likely direction of the conversion between energy components for a large-scale mid-latitude region averaged over the passage of many disturbances. 

In terms of physical processes in the atmosphere, C _K (K _K , A _K ) and C _E (A _E , K _E ) are denominated baroclinic terms because they are strongly related to the processes that presents baroclinic instability (^{Dias, 2010}) or thermal gradients. On the other hand, C _K (K _E , K _Z ) is called barotropic term (^{Asnani, 1993}, ²⁰⁰⁵; ^{Dias, 2010}).

Studies of the energetics of synoptic systems using Lorenz cycle in a limited area (considering the transfer of energy across boundaries) proposed by ^{Muench (1965)} were performed by different authors such as ^{Brennan and Vincent (1980)}, ^{Michaelides (1987)}, and ^{Dias and Da Rocha (2011)} while researching cyclones; ^{Veiga et al. (2013)} used it to study the Walker circulation and its relationship with ENSO; ^{Norquist et al. (1977)} and ^{Hsieh and Cook (2007)} to evaluate African easterly waves; ^{Da Silva and Satyamurty (2013)} in the ITCZ in the South American sector of the Atlantic Ocean; ^{Ramírez et al. (2009)} in a work about the energy of the South American rainy season.

Here, the daily temporal variation of integrated energy components in the atmospheric volume in the ITCZ second band near the Peruvian coast was studied, using the LEC in a new SEP area (SEPn) (from -10º to -2º S and from 91.5º to 81.5º W) (Fig. 3) from January 1 to April 30, 2017.

5.1. Temporal variability of the ITCZ’s second band near the coast

The temporal variability of precipitation, SST, and 10 m wind, as well as its anomalies, averaged between 91.5º and 81.5º W in early 2017 (Fig. 4) shows the presence of the ITCZ second band between the end of January and the beginning of April. The highest intensity of the second band occurred during February and March. The south trade wind relaxation reported by ^{Garreaud (2018)} and ^{Hu et al. (2019)}, even with anomalies from the north, is observed during January, February and March, mainly between 5º N and 10º S, and in April returned to its normality (Fig. 4b).

There were two defined periods with formation of the ITCZ second band, determined only by precipitation anomalies: one from the last days of January to the first half of February, and another during March (purple boxes in Fig. 4b). These periods were preceded by an anomalously warm SST since the beginning of January, and by anomalous winds from the north 10 days before (Fig. 4b). It is possible that the relaxation of the southeast trade winds is associated with the behavior of the South Pacific Anticyclone.

Fig. 4b shows that the surface winds were anomalously from the north between January and March, with two main episodes: the second half of January and March, in the 5º N to 10º S strip. This is similar to ^{Echevin et al. (2018)}, who found that the anomalies of wind stress nearshore and offshore in January 2017 were poleward.

It is observed that the nuclei of maximum precipitation in the ITCZ second band are toward the south of the SST maximum. This is consistent with ^{Gu et al. (2005)}, who found that the precipitation maximum is out of phase toward the poles of the SST maxima.

SST exceeding the threshold of 27 ºC is one of the main factors that favor the development of the ITCZ second band near the coast (mainly when this value is above its normal by 2º C during FM, at least). This threshold is not necessarily required to maintain the first band (Fig. 4). However, a warming of the SST is not sufficient to generate precipitation alone, the behavior of the wind is also important. According to ^{Yu and Zhang (2018)} in the SEP there is no significant relationship between the local SST and precipitation, as there is in the NEP.

In early January, an anomalous westerly wind over the equatorial Pacific was observed, which preceded the formation of the ITCZ second band near the coast between January 31 and February 4, 2017 (Fig. 5). This is congruent with ^{Peng et al. (2019)}), who manifested that these strong westerly winds, which were the largest for January since 1981 (^{Takahashi et al., 2018}), together with anomalous northerly coastal winds, caused the downwelling Kelvin waves, also found by ^{ENFEN (2017a)}.

Fig. 5 (a) Daily SST (ºC, contours), daily precipitation (mm day^-1, shaded) and 10 m wind (m s^-1, vectors). (b) Daily SST anomalies (ºC, contours), daily precipitation anomalies (mm day^-1, shaded) and 10 m wind anomalies (m s^-1, vectors). The values are averaged between 91.5º and 81.5º W. Purple boxes represent the ITCZ second band events. 

Between January 21 and 25 the northerly anomalies in the wind were most prevalent in the analysis region. In the period between February 10-14, the highest intensity of westerly anomalously winds over 110º-90º W was observed, while March was characterized by westerly and northerly anomalous winds (Fig. 5). It is also clear that in the second half of February there was an absence of rainfall in the region.

5.2. Atmospheric circulation

In Fig. 6 we can see that, between January and the first 10 days of February, the MSLP was below its normal in the east of the South Pacific, contrasting with the positive anomaly of MSLP in the equator from 100º W to the west. This contrast of pressure can be associated with the intensification of westerly and northerly winds in the equator close to the Peruvian coast (Fig. 7). This is congruent with ^{Takahashi (2004)}, who suggested that rainy days during 1997-1998 and 2002 El Niño events were associated with an enhanced onshore westerly low-level flow, which may help the triggering of convection by orographic lifting over the western slope of the Andes.

Fig. 6 Five-days mean sea level pressure (hPa, contours) and sea surface temperature (ºC, shaded) anomalies. 

Fig. 7 Five-days precipitation (mm day^-1, shaded) and 10 m wind (m s^-1, vectors) anomalies. Red boxes represent the new SEP area (SEPn). 

After that and until February 24, the MSLP was above its normal in the Southeast Pacific, causing a decrease of rainfall in the second half of February (Fig. 5). Then, between the last days of February and the first half of March, the negative MSLP anomaly in the east of the South Pacific returned, favoring a new increase in rainfall close to the equator, near and over the Peruvian coast. During this period, the MJO was more active and influenced the intensification of surface westerlies in the oriental Pacific near the Equator, as explained in ^{Tang and Yu (2008)}.

The positive SST anomaly near the Peruvian coast was increasing in intensity and area since January 16, which favored the convection producing low-level convergence of the thermally driven boundary layer winds (Lindzen and Nigam, 1987 apud ^{Takahashi, 2004}).

In 600 hPa (Fig. 8), the positive anomalies of mixing ratio (MIXR) in the region of the ITCZ second band near the coast developed around January 21-25, with highest intensity between January 31 and February 4 and positive MIXR flux from east to west. From February 10 to March 1, negative anomalies of MIXR in the region of the ITCZ second band can be observed near the coast, associated with the decrease of rainfall in the second half of February (Figs. 5 and 7). In the first half of March, positive anomalies of MIXR were observed in the region of analysis and the flux was from the west (second band of the ITCZ region) to the east (north of Peru), this is similar to what ^{Sulca et al. (2017)} found for the the ITCZ eastern Pacific configuration (ITCZE).

Fig. 8 Five-days anomalies of mixing ratio in 600 hPa (g kg^-1, shaded) and anomalies of mixing ratio flux in 600 hPa (vectors). 

In upper levels of the troposphere (250 hPa) (Fig. 9) the anomalous configuration of two anticyclonic systems, one north and another south of the equator (better observed between January 31 and February 4) encouraged the positive anomaly of divergence and anomalous easterly winds in the second band of ITCZ near the coastal region and over the north of Peru, similar to ^{Sulca et al. (2017)} and the ITCZE configuration and El Niño 1997-1998 pattern found by ^{Takahashi (2004)} and in CEN 2017 (^{Quispe, 2018}). In the second half of February a decrease in divergence was observed, related to a decrease of rainfall in the same period; and an increase between March 7-16 associated to a positive anomaly of precipitation was observed (Fig. 5).

Fig. 9 Five-days of wind (m s^-1, stream) and divergence anomalies in 250 hPa (s^-1 10^-5, shaded). 

5.3. Relationship between precipitation in the Peruvian northwestern region and the formation of the ITCZ second band

Using TRMM monthly precipitation and the ^{Yu and Zhang (2018)} methodology (considering Ia < 0.5), we identified eight years with maximum precipitation anomalies to the south of the equator: 1998, 1999, 2000, 2001, 2006, 2009, 2012, and 2017. The majority of these years (80%) coincide with the years found by ^{Yu and Zhang (2018)}. The differences may be explained by the climatology and the hierarchical clustering used in this research.

With the aim of identifying the daily ITCZ second band formation, we calculated the Ia index considering the areas proposed by ^{Yu and Zhang (2018)} (Fig. 10, upper panel) and a new proposed area (Fig. 10, lower panel), and compared them with the daily precipitation gauged in the Bernal coastal station (Fig. 10, middle panel). The first day with an important daily precipitation in Bernal (30 mm) was January 30, and the identification of the ITCZ second band (negative Ia) in new proposed areas was on January 19, 11 days prior to the occurrence of a maximum precipitation. This lag would allow anticipating the occurrence of rain on the coast with more than 10 days of advance; however, this is not possible with the Ia calculated in a total area, which showed a negative value on February 6, one week after the first important daily precipitation in Bernal. This lag may be explained by ^{Sulca et al. (2017)}, who showed that the integrated moisture transport in periods with positive ITCZE index (ITCZ for the eastern Pacific) is from the west to the east in northwest Peru; as such, the ITCZ second band formation becomes more important in the prediction of rain in that region, especially if it can be identified with days of anticipation.

Fig. 10 Upper panel: daily Ia index calculated in total areas (considered in ^{Yu and Zhang, 2018}). Middle panel: daily precipitation in the Bernal station (coast of Piura, northwest of Peru). Lower panel: daily Ia index calculated in the new proposed areas. 

5.4. Lorenz energy terms

The daily temporal energy analysis (Fig. 11) shows the greatest increase of K _E and K _Z (K _Z is an order of magnitude more than K _E , similar to what was found in the ITCZ of the Atlantic by ^{Da Silva and Satyamurti [2013}]) in the first half of January, showing an increase of kinetic energy conditions since early January due to the intensification of wind velocity. Other peaks of K _E were present in the first half of February and March, but with values close to half of those obtained in January. This decrease in K _E can be related to the presence of a CEN event, which was also found by ^{Veiga et al. (2013)} and ^{Sátyro and Veiga (2017)} in warm ENSO episodes, due to the decrease in the transfer of K _E from the environment to the area of the second band, as the warming generated by CEN in the entire eastern Pacific region near Peru did not allow for significant thermal gradients that generate energy transfer. The peaks of K _E in the first half of February and March are related to maximums of precipitation in the ITCZ second band (Fig. 5), which can be explained by the increased of convection during this period.

Fig. 11 Time series of volume-integrated Lorenz energy terms (K _Z × 10⁴, K _E × 10³, A _Z × 10³ and A _E × 10³) in the SEPn area (values in J m^-2). 

Values of A _Z and A _E are smaller than K _E and K _Z (similar to ^{Da Silva and Satyamurti [2013}] for the south Atlantic ITCZ) in the equator regions as the horizontal thermal variations are not significant. The peaks of A _E and A _Z (the former was greater than the latter) are registered in January and in the first 10 days of March, indicating that, in these days, the thermal gradients in the same latitude were greater than the meridional temperature gradients. Physically, the peaks of A _E and A _Z on January can be explained by the meridional and zonal thermal gradients in the lower troposphere and sea surface; then, in the first half of March, as it gradually warms up because the CEN occurrence, the convection became important because it generated thermal differences in regions in the same latitude, increasing the values of A _E .

Figure 12 shows that among all types of energy conversion, C _A (conversion of A _Z in A _E ) has the smallest order of magnitude, followed by C _Z (conversion of K _Z in A _Z ), which is due to very small horizontal thermal gradients in the ITCZ region. On the other hand, similar to ^{Da Silva and Satyamurti (2013)}, C _E (conversion of A _E in K _E ) and C _K (conversion of K _E in K _Z ) have the same order of magnitude, as the barotropic instability has a great contribution in equatorial regions.

Fig. 12 Time series of volume-integrated energy conversions of the Lorenz energy cycle (C _A × 10^-2, C _Z × 10^-1, C _K × 10⁰ and C _E × 10⁰) in SEPn area (values in W m^-2). 

The conversion from A _E to A _Z (negative C _A ) in January, in the second half of February and in the second half of March ahead indicates that, due to the northerly motions, the zonal thermal variations slightly increase the thermal gradient between latitudes and generates A _Z gain. Contrary, positive C _A in the first half of February and March (periods with more convection) indicate transport of warm tropical air to polar latitudes and cold polar air to warm latitudes through meridional motions. This transport could be enhanced by the ascending movements in the convergence zone and subsident movements over southern regions.

The barotropic process (C _K ) has high values in January and the first half of February, with positive values indicating conversion from K _E to K _Z . Considering this process, the increase of K _Z observed in the first half of January in Figure 11 is due, mainly, to the energy transferred from the eddies (K _E ).

On the other hand, C _Z has more variability, mainly in February and March, oscillating between negative and positive values, changing the flux of conversion, manifesting the similar importance of K _Z and A _Z during the convection of ITCZ second band region. CE has only positive values, with a maximum in the second half of March, indicating that the increase of K _E observed in this period in Figure 11 is due to conversion from A _E .

At the boundaries, the flux of A _Z has the smallest order of magnitude, related to minimum horizontal variations of temperature in the equatorial region (Fig. 13).

Fig. 13 Time series of volume-integrated boundary energy transports of the Lorenz energy cycle (BA _Z × 10^-1) in SEPn area (values in W m^-2). 

The flux of kinetic energy (K _Z and K _E ) is from the exterior to the area of the ITCZ second band (positive values) in January and the first half of February; as a result, part of maximums of K _Z and K _E observed in this period were obtained from the environment. During the rest of the period of the study, the transfer of kinetic energy from the boundaries is almost null.

In the case of the flux of A _E , almost all values are positive, indicating flux from the exterior to the area of the ITCZ, with a maximum around January 15. While the flux of A _Z has values oscillating between positive and negative, indicating, mainly, flux from exterior to the ITCZ second band region in the second half of January, and flux in the opposite direction in the first half of January and early March, possibly due to the greater warming of the ITCZ second band region compared to its surroundings.