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## Abstract

In meteorology and oceanography, and other fields, it is often necessary to fit a straight line to some points and estimate its slope. If both variables corresponding to the points are noisy, the slope as estimated by the ordinary least squares regression coefficient is biased low; that is, for a large enough sample, it *always* underestimates the true regression coefficient between the variables. In the common situation when the relative size of the noise in the variables is unknown, an appropriate regression coefficient is plus or minus the ratio of the standard deviations of the variables, the sign being determined by the sign of the correlation coefficient. For this case of unknown noise, the authors here obtain the probability density function (pdf) for the true regression coefficient divided by the appropriate regression coefficient just mentioned. For the case when the number of data is very large, a simple analytical expression for this pdf is obtained; for a finite number of data points the relevant pdfs are obtained numerically. The pdfs enable the authors to provide tables for confidence intervals for the true regression coefficient. Using these tables, the end result of this analysis is a simple practical way to estimate the true regression coefficient between two variables given their standard deviations, the sample correlation, and the number of independent data.

## Abstract

In meteorology and oceanography, and other fields, it is often necessary to fit a straight line to some points and estimate its slope. If both variables corresponding to the points are noisy, the slope as estimated by the ordinary least squares regression coefficient is biased low; that is, for a large enough sample, it *always* underestimates the true regression coefficient between the variables. In the common situation when the relative size of the noise in the variables is unknown, an appropriate regression coefficient is plus or minus the ratio of the standard deviations of the variables, the sign being determined by the sign of the correlation coefficient. For this case of unknown noise, the authors here obtain the probability density function (pdf) for the true regression coefficient divided by the appropriate regression coefficient just mentioned. For the case when the number of data is very large, a simple analytical expression for this pdf is obtained; for a finite number of data points the relevant pdfs are obtained numerically. The pdfs enable the authors to provide tables for confidence intervals for the true regression coefficient. Using these tables, the end result of this analysis is a simple practical way to estimate the true regression coefficient between two variables given their standard deviations, the sample correlation, and the number of independent data.

## Abstract

*B*(

*t*) embedded in the Southern Oscillation index. The analysis shows that the Southern Oscillation index

*S*(

*t*) may be written

*S*

*t*

*B*

*t*

*L*

*t*

*M*

*t*

*B*(

*t*) has a zero in May and

*L*(

*t*) and

*M*(

*t*) vary interannually and decadally. Since

*L*is time dependent with negligible mean

*S*(

*t*) does not have a biennial peak even though

*B*(

*t*) is present. The persistence barrier strengthens and weakens decadally as

*L*and

*M*vary decadally. For example, during 1975–84

*BL*dominates

*M*and the persistence barrier is strong while for the decade 1940–49

*BL*is negligible and the persistence barrier disappears.

## Abstract

*B*(

*t*) embedded in the Southern Oscillation index. The analysis shows that the Southern Oscillation index

*S*(

*t*) may be written

*S*

*t*

*B*

*t*

*L*

*t*

*M*

*t*

*B*(

*t*) has a zero in May and

*L*(

*t*) and

*M*(

*t*) vary interannually and decadally. Since

*L*is time dependent with negligible mean

*S*(

*t*) does not have a biennial peak even though

*B*(

*t*) is present. The persistence barrier strengthens and weakens decadally as

*L*and

*M*vary decadally. For example, during 1975–84

*BL*dominates

*M*and the persistence barrier is strong while for the decade 1940–49

*BL*is negligible and the persistence barrier disappears.

## Abstract

An analytical method for computing the speed at which the nose of a light (rotating) intrusion advances along a continental shelf is proposed. The nonlinear model includes two active layer; the intrusion itself, which occupies the entire shelf (and extends beyond the shelf break), and the heavy fluid situated both ahead of the intrusion and in the deep ocean. The section of the intrusion which extends beyond the shelf break overlies an infinitely deep ocean. Friction is neglected but the motions near the intrusion's leading edge are not constrained to be quasi-geostrophic nor are they constrained to be hydrostatic.

Solutions for steadily propagating currents are constructed analytically by taking into account the flow-forces behind and ahead of the nose, and considering the conservation of energy and potential vorticity. This procedure leads to a set of algebraic equation which are solved analytically using a perturbation scheme in ε, the ratio between the internal deformation radius and the shelf width.

It is found that all the heavy fluid ahead of the intrusion is *trapped* and cannot be removed from the shelf. Namely, it is pushed ahead of the intrusion's leading edge as the gravity current is advancing behind. Unlike intrusions without a shelf, which can never reach a truly steady propagation rate (in an infinitely deep ocean), the intrusion in question propagates *steadily* when ε → 0. Under such conditions, the propagation rate is given by (2*g*′*D*)^{½}, where *g*′ is the “reduced gravity” and *D* is the intrusion depth at the shelf break [note that *D* ≥ *H*, where *H* is the (uniform) shelf depth, so that at the shelf break the intrusion is deeper than the shelf].

Possible applications of this theory to various oceanic situations, such as the Skagerrak outflow, are mentioned.

## Abstract

An analytical method for computing the speed at which the nose of a light (rotating) intrusion advances along a continental shelf is proposed. The nonlinear model includes two active layer; the intrusion itself, which occupies the entire shelf (and extends beyond the shelf break), and the heavy fluid situated both ahead of the intrusion and in the deep ocean. The section of the intrusion which extends beyond the shelf break overlies an infinitely deep ocean. Friction is neglected but the motions near the intrusion's leading edge are not constrained to be quasi-geostrophic nor are they constrained to be hydrostatic.

Solutions for steadily propagating currents are constructed analytically by taking into account the flow-forces behind and ahead of the nose, and considering the conservation of energy and potential vorticity. This procedure leads to a set of algebraic equation which are solved analytically using a perturbation scheme in ε, the ratio between the internal deformation radius and the shelf width.

It is found that all the heavy fluid ahead of the intrusion is *trapped* and cannot be removed from the shelf. Namely, it is pushed ahead of the intrusion's leading edge as the gravity current is advancing behind. Unlike intrusions without a shelf, which can never reach a truly steady propagation rate (in an infinitely deep ocean), the intrusion in question propagates *steadily* when ε → 0. Under such conditions, the propagation rate is given by (2*g*′*D*)^{½}, where *g*′ is the “reduced gravity” and *D* is the intrusion depth at the shelf break [note that *D* ≥ *H*, where *H* is the (uniform) shelf depth, so that at the shelf break the intrusion is deeper than the shelf].

Possible applications of this theory to various oceanic situations, such as the Skagerrak outflow, are mentioned.

## Abstract

Friction, the alongshore pressure gradient and time-dependent effects are all of lowest-order importance in the dynamics of wind-driven fluctuating currents and sea levels on continental shelves. Previous work has shown that when all these effects are included, the ocean response can be described by an infinite sum of coastal- trapped waves whose amplitudes satisfy a fully coupled infinite set of forced, first-order wave equations. We present a practical method for solving this coupled set of equations for general low-frequency, large-scale wind stress forcing as input. Convergence properties of the solution are examined analytically. For the same accuracy, more modes are required to describe alongshore currents than sea level and fewer modes are required to describe barotropic than depth-dependent motion.

As an example, numerical calculations were carried out for a model of the West Florida Shelf. The sea level field was effectively described by one mode but the alongshore velocity field was not Seven modes were necessary to represent the solution accurately. Decoupling the equations by setting off diagonal elements of the friction coupling coefficients equal to zero significantly changed the alongshore velocity amplitude. For realistic parameter values the Gill and Schumann functionless alongshore velocity field and the Arrested-Topographic Wave alongshore velocity field differed significantly from that of the more general case.

## Abstract

Friction, the alongshore pressure gradient and time-dependent effects are all of lowest-order importance in the dynamics of wind-driven fluctuating currents and sea levels on continental shelves. Previous work has shown that when all these effects are included, the ocean response can be described by an infinite sum of coastal- trapped waves whose amplitudes satisfy a fully coupled infinite set of forced, first-order wave equations. We present a practical method for solving this coupled set of equations for general low-frequency, large-scale wind stress forcing as input. Convergence properties of the solution are examined analytically. For the same accuracy, more modes are required to describe alongshore currents than sea level and fewer modes are required to describe barotropic than depth-dependent motion.

As an example, numerical calculations were carried out for a model of the West Florida Shelf. The sea level field was effectively described by one mode but the alongshore velocity field was not Seven modes were necessary to represent the solution accurately. Decoupling the equations by setting off diagonal elements of the friction coupling coefficients equal to zero significantly changed the alongshore velocity amplitude. For realistic parameter values the Gill and Schumann functionless alongshore velocity field and the Arrested-Topographic Wave alongshore velocity field differed significantly from that of the more general case.

## Abstract

Sea-level measurements along the western coast of the Americas have shown that there is a strong signal at ENSO frequencies (approximately 2π/2 yr^{−1} to 2π/5 yr^{−1}) that propagates poleward at about 40 to 90 cm s^{−1}. This ENSO sea level signal must be associated with ENSO coastal currents, but because adequate interannual current time series are unavailable, the structure and strength of these currents are not known. Coastal ENSO currents must be fundamentally affected by bottom topography and bottom friction, but previous theory has not taken these effects into account. A near-boundary numerical model with realistic bottom friction, stratification, and shelf and slope topography was therefore constructed to study ENSO coastal flow.

(i) At ENSO frequencies, previous results for models with no bottom topography and no bottom friction suggest that sea level should not propagate poleward. With realistic bottom friction and bottom topography coastal sea level propagates poleward at speeds similar to those observed. A simple mechanism based on the effect of bottom friction on offshore propagating geostrophic alongshore flow explains why coastal poleward alongshore propagation occurs. Calculations also show that the depths of the 20°C and 15°C isotherms also propagate poleward at approximately the observed speeds.

(ii) Sea levels change little across the shelf and slope at lower latitudes and slowly decrease in amplitude alongshore due to bottom friction. The small sea level change across the shelf and slope implies that the long sea level records available are useful for analysing the nearby deep ocean variability.

(iii) Lower-order deep-sea vertical modes incident at the equator are rapidly scattered mainly by bottom friction into other (higher) vertical modes. Scattering has two main effects. Those vertical modes equatorward of their critical latitudes propagate offshore as Rossby waves interfere with each other and produce a complicated deep-sea velocity field, especially at low latitudes where most of the vertical modes are propagating offshore. Those vertical modes poleward of their critical latitudes only exist as coastally trapped motion and give rise to a trapped ENSO jet over the continental slope. This jet has an amplitude peak of order 20 cm s^{−1} and is trapped within about 500 m of the bottom. The jet core is approximately 180° out of phase with near-surface currents over the continental shelf and slope. Therefore, during (say) the El Niño part of the ENSO cycle when the sea level is high and the near-surface flow over the continental shelf and slope tends to be poleward, the flow in the jet core tends to be equatorward. Present observations are inadequate to prove or disprove the existence of this ENSO continental slope jet. Due to bottom friction, the alongshore velocity decreases shoreward of the shelf break and is negligible at the coast.

(iv) Critical latitudes for vertical modes change when the coastline angle changes and so motion near the boundary is affected by coastline angle. When the coastline is less meridional, coastal sea level and the 20°C and 15°C isotherm depths propagate poleward more rapidly (although still at approximately the observed speeds). The ENSO jet has its maximum amplitude nearer the equator.

(v) In the biologically important top 100 m or so of the ocean alongshore particle displacements seaward of the shelf can be ∼1000 km. Interannual near-surface alongshore currents over the continental shelf and slope lead coastal sea level by several months.

## Abstract

Sea-level measurements along the western coast of the Americas have shown that there is a strong signal at ENSO frequencies (approximately 2π/2 yr^{−1} to 2π/5 yr^{−1}) that propagates poleward at about 40 to 90 cm s^{−1}. This ENSO sea level signal must be associated with ENSO coastal currents, but because adequate interannual current time series are unavailable, the structure and strength of these currents are not known. Coastal ENSO currents must be fundamentally affected by bottom topography and bottom friction, but previous theory has not taken these effects into account. A near-boundary numerical model with realistic bottom friction, stratification, and shelf and slope topography was therefore constructed to study ENSO coastal flow.

(i) At ENSO frequencies, previous results for models with no bottom topography and no bottom friction suggest that sea level should not propagate poleward. With realistic bottom friction and bottom topography coastal sea level propagates poleward at speeds similar to those observed. A simple mechanism based on the effect of bottom friction on offshore propagating geostrophic alongshore flow explains why coastal poleward alongshore propagation occurs. Calculations also show that the depths of the 20°C and 15°C isotherms also propagate poleward at approximately the observed speeds.

(ii) Sea levels change little across the shelf and slope at lower latitudes and slowly decrease in amplitude alongshore due to bottom friction. The small sea level change across the shelf and slope implies that the long sea level records available are useful for analysing the nearby deep ocean variability.

(iii) Lower-order deep-sea vertical modes incident at the equator are rapidly scattered mainly by bottom friction into other (higher) vertical modes. Scattering has two main effects. Those vertical modes equatorward of their critical latitudes propagate offshore as Rossby waves interfere with each other and produce a complicated deep-sea velocity field, especially at low latitudes where most of the vertical modes are propagating offshore. Those vertical modes poleward of their critical latitudes only exist as coastally trapped motion and give rise to a trapped ENSO jet over the continental slope. This jet has an amplitude peak of order 20 cm s^{−1} and is trapped within about 500 m of the bottom. The jet core is approximately 180° out of phase with near-surface currents over the continental shelf and slope. Therefore, during (say) the El Niño part of the ENSO cycle when the sea level is high and the near-surface flow over the continental shelf and slope tends to be poleward, the flow in the jet core tends to be equatorward. Present observations are inadequate to prove or disprove the existence of this ENSO continental slope jet. Due to bottom friction, the alongshore velocity decreases shoreward of the shelf break and is negligible at the coast.

(iv) Critical latitudes for vertical modes change when the coastline angle changes and so motion near the boundary is affected by coastline angle. When the coastline is less meridional, coastal sea level and the 20°C and 15°C isotherm depths propagate poleward more rapidly (although still at approximately the observed speeds). The ENSO jet has its maximum amplitude nearer the equator.

(v) In the biologically important top 100 m or so of the ocean alongshore particle displacements seaward of the shelf can be ∼1000 km. Interannual near-surface alongshore currents over the continental shelf and slope lead coastal sea level by several months.

## Abstract

A different way of looking at the meridional warm water (*σ*
_{
θ
} < 26.8) flux in the South and North Atlantic is proposed. The approach involves the blending of observational aspects into analytical modeling, which allows one to circumvent finding a detailed solution to the complete wind–thermohaline problem. The method employs an integration of the momentum equations along a “horseshoe” path in a rectangular basin that is open on the southern side.

The initial model considered involves a northward flowing upper layer, a stagnant intermediate layer, and a southward flowing deep layer. By choosing the integration path to begin at one separation point (the Brazil Current separation from South America) and end at another separation point (the Gulf Stream separation), a rather simple expression for the meridional upper-layer transport (*T*) is obtained. In this scenario the high-latitude cooling affects the warm water northward transport through its influence on the latitude of the western boundary current separation.

The authors find that the combined transport (i.e., the transport induced by both wind and high-latitude cooling) is given by *T* = ∫ (*τ*
^{
l
}/*ρ*) *dl*/(*f*
_{1} − *f*
_{2}), where *f*
_{1} and *f*
_{2} are the Coriolis parameters along the northern and southern separation latitudes (i.e., *f*
_{2} < 0), and *τ*
^{
l
} is the wind stress along the integration path (*l*). The amount of high-latitude cooling that causes the deep-water formation in the North Atlantic does not enter this relationship explicitly but it does enter the calculations implicitly (through the position of the separation points that adjust to the cooling). Process-oriented numerical experiments, which were conducted using MICOM, are in excellent agreement with the above formula.

Surprisingly, application of the formula to the Atlantic gives a transport of less than one Sverdrup (Sv ≡ 10^{6} m^{3} s^{−1}), an amount that is insignificant compared to the frequently quoted values (10–20 Sv). This questions the common suggestion that surface Atlantic Water flows northward and sinks in high latitude due to wind and high-latitude cooling *alone.* The difficulty is resolved when a *low* or *midlatitude* conversion of Atlantic Intermediate Water to upper thermocline water (via upwelling) is added (à la Goldsbrough) to the model. This implies that the upwelling needed to balance the deep-water formation in the North Atlantic must occur within the limits of the Atlantic Ocean itself rather than in the Pacific and the Indian Oceans. An additional point of interest is that the inclusion of upwelling does not show that all the upwelled water ultimately sinks in the North Atlantic. Rather, it shows that any amount of upwelled intermediate water (at low and midlatitudes) must be *equally split* between a flow that exits the northern gyre on the north side and a flow that exits the South Atlantic somewhere along the section connecting the mean position of the Brazil Current separation point and the tip of South Africa.

## Abstract

A different way of looking at the meridional warm water (*σ*
_{
θ
} < 26.8) flux in the South and North Atlantic is proposed. The approach involves the blending of observational aspects into analytical modeling, which allows one to circumvent finding a detailed solution to the complete wind–thermohaline problem. The method employs an integration of the momentum equations along a “horseshoe” path in a rectangular basin that is open on the southern side.

The initial model considered involves a northward flowing upper layer, a stagnant intermediate layer, and a southward flowing deep layer. By choosing the integration path to begin at one separation point (the Brazil Current separation from South America) and end at another separation point (the Gulf Stream separation), a rather simple expression for the meridional upper-layer transport (*T*) is obtained. In this scenario the high-latitude cooling affects the warm water northward transport through its influence on the latitude of the western boundary current separation.

The authors find that the combined transport (i.e., the transport induced by both wind and high-latitude cooling) is given by *T* = ∫ (*τ*
^{
l
}/*ρ*) *dl*/(*f*
_{1} − *f*
_{2}), where *f*
_{1} and *f*
_{2} are the Coriolis parameters along the northern and southern separation latitudes (i.e., *f*
_{2} < 0), and *τ*
^{
l
} is the wind stress along the integration path (*l*). The amount of high-latitude cooling that causes the deep-water formation in the North Atlantic does not enter this relationship explicitly but it does enter the calculations implicitly (through the position of the separation points that adjust to the cooling). Process-oriented numerical experiments, which were conducted using MICOM, are in excellent agreement with the above formula.

Surprisingly, application of the formula to the Atlantic gives a transport of less than one Sverdrup (Sv ≡ 10^{6} m^{3} s^{−1}), an amount that is insignificant compared to the frequently quoted values (10–20 Sv). This questions the common suggestion that surface Atlantic Water flows northward and sinks in high latitude due to wind and high-latitude cooling *alone.* The difficulty is resolved when a *low* or *midlatitude* conversion of Atlantic Intermediate Water to upper thermocline water (via upwelling) is added (à la Goldsbrough) to the model. This implies that the upwelling needed to balance the deep-water formation in the North Atlantic must occur within the limits of the Atlantic Ocean itself rather than in the Pacific and the Indian Oceans. An additional point of interest is that the inclusion of upwelling does not show that all the upwelled water ultimately sinks in the North Atlantic. Rather, it shows that any amount of upwelled intermediate water (at low and midlatitudes) must be *equally split* between a flow that exits the northern gyre on the north side and a flow that exits the South Atlantic somewhere along the section connecting the mean position of the Brazil Current separation point and the tip of South Africa.

## Abstract

Recent general circulation simulations suggest that, prior to the closure of the Panama Isthmus (the narrow strip of land connecting North and South America), low-salinity Pacific Ocean water invaded the Atlantic Ocean via the gap between North and South America. According to this scenario, the invasion decreased the Atlantic Ocean salinity to the point at which North Atlantic Deep Water (NADW) formation was impossible and, consequently, there was probably no “conveyer belt.” In line with this scenario, it has been suggested that the closure of the isthmus led to an increased salinity in the Atlantic that, in turn, led to the present-day NADW formation and the familiar meridional overturning cell (MOC). Using simple dynamical principles, analytical modeling, process-oriented numerical experiments, and modern-day wind stress, it is shown that, in the absence of NADW formation, one would expect a *westward* flow from the Atlantic to the Pacific Ocean through an open Panama Isthmus. This contradicts the suggestion made by the earlier numerical models that imply an eastward flow through the “Panama Gateway.” An analogous present-day situation (for a system without deep-water formation) is that of the Indonesian Throughflow, which brings Pacific water to the Indian Ocean rather than the other way around; that is, it is also a westward flow rather than an eastward flow. “Island rule” calculations clearly show that the direction of the flow in both situations is determined by the wind field to the east of the gaps. The authors show that exceptionally strong vertical mixing in the Atlantic (as compared with the Pacific) or another means of warm-water removal from the upper layer in the Atlantic (e.g., NADW or strong cooling) could reverse the direction of the flow through the open isthmus. This is most likely what happened in the earlier numerical simulation, which must have invoked (explicitly or implicitly) large quantities of upper-water removal even without NADW formation. On this basis it is suggested that if low-salinity Pacific water did, in fact, invade the Atlantic Ocean prior to the closure of the Panama Isthmus, then this invasion took place via the Bering Strait rather than through the open Panama Isthmus. It is also suggested that, if there were 20 Sv (Sv ≡ 10^{6} m^{3} s^{−1}) of NADW formation today and the Panama Isthmus were to be suddenly open today, then Pacific water would indeed invade the Atlantic via the Panama Gateway. In turn, this would either collapse the existing NADW formation rate or reduce it to about 10 Sv, which can be maintained even with an open isthmus. In both cases the final outcome is a westward flow in the open isthmus.

## Abstract

Recent general circulation simulations suggest that, prior to the closure of the Panama Isthmus (the narrow strip of land connecting North and South America), low-salinity Pacific Ocean water invaded the Atlantic Ocean via the gap between North and South America. According to this scenario, the invasion decreased the Atlantic Ocean salinity to the point at which North Atlantic Deep Water (NADW) formation was impossible and, consequently, there was probably no “conveyer belt.” In line with this scenario, it has been suggested that the closure of the isthmus led to an increased salinity in the Atlantic that, in turn, led to the present-day NADW formation and the familiar meridional overturning cell (MOC). Using simple dynamical principles, analytical modeling, process-oriented numerical experiments, and modern-day wind stress, it is shown that, in the absence of NADW formation, one would expect a *westward* flow from the Atlantic to the Pacific Ocean through an open Panama Isthmus. This contradicts the suggestion made by the earlier numerical models that imply an eastward flow through the “Panama Gateway.” An analogous present-day situation (for a system without deep-water formation) is that of the Indonesian Throughflow, which brings Pacific water to the Indian Ocean rather than the other way around; that is, it is also a westward flow rather than an eastward flow. “Island rule” calculations clearly show that the direction of the flow in both situations is determined by the wind field to the east of the gaps. The authors show that exceptionally strong vertical mixing in the Atlantic (as compared with the Pacific) or another means of warm-water removal from the upper layer in the Atlantic (e.g., NADW or strong cooling) could reverse the direction of the flow through the open isthmus. This is most likely what happened in the earlier numerical simulation, which must have invoked (explicitly or implicitly) large quantities of upper-water removal even without NADW formation. On this basis it is suggested that if low-salinity Pacific water did, in fact, invade the Atlantic Ocean prior to the closure of the Panama Isthmus, then this invasion took place via the Bering Strait rather than through the open Panama Isthmus. It is also suggested that, if there were 20 Sv (Sv ≡ 10^{6} m^{3} s^{−1}) of NADW formation today and the Panama Isthmus were to be suddenly open today, then Pacific water would indeed invade the Atlantic via the Panama Gateway. In turn, this would either collapse the existing NADW formation rate or reduce it to about 10 Sv, which can be maintained even with an open isthmus. In both cases the final outcome is a westward flow in the open isthmus.

## Abstract

The authors develop a method for the long-lead forecasting of El Niño–influenced rainfall probability and illustrate it using the economically important prediction, from the beginning of the year, of September–November (SON) rainfall in the coastal sugarcane producing region of Australia’s northeastern coast. The method is based on two probability distributions. One is the Gaussian error distribution of the long-lead prediction of the El Niño index Niño-3.4 by the Clarke and Van Gorder forecast method. The other is the relationship of the rainfall distribution to the Niño-3.4 index. The rainfall distribution can be approximated by a gamma distribution whose two parameters depend on Niño-3.4. To predict the rainfall at, say, the Tully Sugar, Ltd., mill on the north Queensland coast in SON 2009, the June–August (JJA) value of Niño-3.4 is predicted and then 1000 possible “observed” JJA Niño-3.4 values calculated from the error distribution. Each one of these observed Niño-3.4 values is then used, with the Niño-3.4-dependent gamma distribution for that location, to calculate 1000 possible SON rainfall totals. The result is one million possible SON rainfalls. A histogram of these rainfalls is the required probability distribution for the rainfall at that location predicted from the beginning of the year. Cross-validated predictions suggest that the method is successful.

## Abstract

The authors develop a method for the long-lead forecasting of El Niño–influenced rainfall probability and illustrate it using the economically important prediction, from the beginning of the year, of September–November (SON) rainfall in the coastal sugarcane producing region of Australia’s northeastern coast. The method is based on two probability distributions. One is the Gaussian error distribution of the long-lead prediction of the El Niño index Niño-3.4 by the Clarke and Van Gorder forecast method. The other is the relationship of the rainfall distribution to the Niño-3.4 index. The rainfall distribution can be approximated by a gamma distribution whose two parameters depend on Niño-3.4. To predict the rainfall at, say, the Tully Sugar, Ltd., mill on the north Queensland coast in SON 2009, the June–August (JJA) value of Niño-3.4 is predicted and then 1000 possible “observed” JJA Niño-3.4 values calculated from the error distribution. Each one of these observed Niño-3.4 values is then used, with the Niño-3.4-dependent gamma distribution for that location, to calculate 1000 possible SON rainfall totals. The result is one million possible SON rainfalls. A histogram of these rainfalls is the required probability distribution for the rainfall at that location predicted from the beginning of the year. Cross-validated predictions suggest that the method is successful.

## Abstract

Many investigators have noted strong biennial atmospheric and oceanic variability, phase-locked to the calendar year, over the equatorial Indian and Pacific Oceans. A simple air–sea interaction theory suggests that biennial oscillations in the far western equatorial Pacific (120°–140°E) may originate from an air–sea interaction instability involving the mean seasonal wind cycle and evaporation. Over a wide range of realistic parameters the instability grows rapidly and is phase-locked to the calendar year in a similar way to the observations. Crucial to the mechanism are that the anomalous equatorial surface wind response is westerly under anomalous deep convection, that it lags the convection by at least 1 month, and that the zonal seasonal wind has a strong 12-month cycle.

No such air–sea interaction instability is possible in the equatorial Indian Ocean because the water is either too cold for deep convection most of the year (western equatorial Indian Ocean, 40°–60°E) or the wind is westerly nearly all the year (central and eastern equatorial Indian Ocean 60°–100°E). Yet strong biennial oscillations occur in the central and eastern equatorial Indian Ocean. A second simple model suggests that the western equatorial Pacific biennial oscillation remotely drives these.

## Abstract

Many investigators have noted strong biennial atmospheric and oceanic variability, phase-locked to the calendar year, over the equatorial Indian and Pacific Oceans. A simple air–sea interaction theory suggests that biennial oscillations in the far western equatorial Pacific (120°–140°E) may originate from an air–sea interaction instability involving the mean seasonal wind cycle and evaporation. Over a wide range of realistic parameters the instability grows rapidly and is phase-locked to the calendar year in a similar way to the observations. Crucial to the mechanism are that the anomalous equatorial surface wind response is westerly under anomalous deep convection, that it lags the convection by at least 1 month, and that the zonal seasonal wind has a strong 12-month cycle.

No such air–sea interaction instability is possible in the equatorial Indian Ocean because the water is either too cold for deep convection most of the year (western equatorial Indian Ocean, 40°–60°E) or the wind is westerly nearly all the year (central and eastern equatorial Indian Ocean 60°–100°E). Yet strong biennial oscillations occur in the central and eastern equatorial Indian Ocean. A second simple model suggests that the western equatorial Pacific biennial oscillation remotely drives these.