What exactly IS ACE trying to measure from a physics standpoint?

[Team Ghost]

ACE is defined to be the sum of squares of the maximum sustained wind speed of a tropical cyclone at 6-hour intervals such that the maximum sustained wind speed of the tropical cyclone is at minimum 35 kt.

More succinctly, ACE = Σv_s^2, where v_s is the maximum sustained wind speed at a synoptic point such that v is greater than or equal to 35 kt.

ACE stands for “accumulated cyclone energy”, but I fail to see what about this is measuring the energy of a tropical cyclone.

Is it the kinetic energy of a cyclone? The kinetic energy K of a point mass whose mass is m moving with a velocity v is K = 1/2mv^2; for a continuous body, this becomes dK = 1/2v^2dm. Since our world has 3 spatial dimensions, dK = 1/2v^2ρdV, where ρ is the mass density of the cyclone. If 1/2v^2ρdV were integrated over the entire volume of the cyclone, the result would be the total kinetic energy of the cyclone, but this does not correspond at all to the formula for ACE because (a) the formula for ACE does not take into account the mass of the tropical cyclone and (b) the formula for the kinetic energy of the cyclone does not depend on the duration the cyclone lasted.

Is it the power dissipated by a cyclone (which is what PDI tries to measure)? For an object off surface area A and drag coefficient C moving with velocity v relative to a fluid of density ρ, the drag force experienced is F = -1/2CρAv^2v̂. The power P exerted by a force F onto an object moving with velocity v is P = F • v. Combining these two equations gives us that the power exerted by the drag force onto an object is P = -1/2CρAv^3; expressed differently, the power dissipated by a tropical cyclone is P_dissipated = 1/2CρAv^3; differentiating both sides gives dP_dissipated = 1/2Cρv^3dA. 1/2Cρv^3dA integrated over the wind field of the tropical cyclone at any given point in time gives the power dissipated by the tropical cyclone at that point in time, and since E = dP/dt, 1/2Cρv^3dAdt integrated first over the wind field as a function of time and then integrated over the lifespan of the tropical cyclone gives the total energy dissipated by the hurricane. Still, this is not quite like for the formula for ACE because while it does account for the duration of the tropical cyclone (albeit with an extra time dimension), it (a) scales with v^2 instead of v^3 and (b) takes into account the wind field of the tropical cyclone, which ACE does not.

If ACE measures neither of the above, what does it measure?

[Category5Kaiju]

ACE is, in a certain sense, a rather simplistic way of measuring the quality of a cyclone, both in terms of strength and duration. You're right in that the formula for ACE is 10^-4 times (the sum of vmax squared), for vmax values greater than or equal to 34 knots. Based on this formula, the ACE equation heavily favors systems that are strong, as the ACE value for a Category 4+ hurricane that maintains this strength for 3 days, for example, is MUCH greater than a tropical storm that maintains such strength for 3 days.

As you can tell from this equation alone, there's really not an "energy" component to this. The equation's components and its output don't have anything related to Joules, the SI unit for energy. This is why I personally think that calling it "ACE" might be somewhat confusing to people who are very knowledgable about physics. Instead, something like "accumulated cyclone quality"/"ACQ" or "cyclone quality conversion factor"/"CQCF" would be more appropriate, at least imho.

[Team Ghost]

ACE is, in a certain sense, a rather simplistic way of measuring the quality of a cyclone, both in terms of strength and duration. You're right in that the formula for ACE is 10^-4 times (the sum of vmax squared), for vmax values greater than or equal to 34 knots. Based on this formula, the ACE equation heavily favors systems that are strong, as the ACE value for a Category 4+ hurricane that maintains this strength for 3 days, for example, is MUCH greater than a tropical storm that maintains such strength for 3 days.

As you can tell from this equation alone, there's really not an "energy" component to this. The equation's components and its output don't have anything related to Joules, the SI unit for energy. This is why I personally think that calling it "ACE" might be somewhat confusing to people who are very knowledgable about physics. Instead, something like "accumulated cyclone quality"/"ACQ" or "cyclone quality conversion factor"/"CQCF" would be more appropriate, at least imho.

Is there a physical quantity about a tropical cyclone that ACE is trying to measure? It seems to me that ACE is trying to approximate the integral of 1/T_synoptic*v_max^2dt over a storm’s lifespan, where T_synoptic is the duration between synoptic points and v_max is the maximum sustained wind speed of the storm. I have trouble seeing what physical quantity this is and why it is necessary to divide out T_synoptic.

If this measures the “quality” of a cyclone, my biggest question is why it is defined as so. Why is ACE not Σv_max? Why is ACE not Σv_max^3? What is so special about Σv_max^2? I know v^2 appears in the expression for kinetic energy, but ACE approximates 2/(m*T_synoptic)∫Kdt.

While writing this post, I realized that, in a sense ∫Kdt is a useful quantity. You can in principle define a Lagrangian L = K - U (kinetic energy minus potential energy) and compute the action S = ∫Ldt, and action is a useful physical quantity; the kinetic energy of a cyclone, as shown in the original post, is given by K = 1/2∭ρ*v_max^2dV, and if gravity is assumed to be the only force acting on a tropical cyclone(i.e. assuming zero friction or drag), the potential energy of a tropical cyclone is given by U = ∭ρ*g*ydV. Since it is always possible to pick a value of y so that U = 0, it is always possible to pick a value of y such that L = K, and so ∫Kdt really would be the action of the tropical cyclone over its lifetime. I wonder if this is what ACE is trying very crudely to approximate.

[Category5Kaiju]

ACE is, in a certain sense, a rather simplistic way of measuring the quality of a cyclone, both in terms of strength and duration. You're right in that the formula for ACE is 10^-4 times (the sum of vmax squared), for vmax values greater than or equal to 34 knots. Based on this formula, the ACE equation heavily favors systems that are strong, as the ACE value for a Category 4+ hurricane that maintains this strength for 3 days, for example, is MUCH greater than a tropical storm that maintains such strength for 3 days.

As you can tell from this equation alone, there's really not an "energy" component to this. The equation's components and its output don't have anything related to Joules, the SI unit for energy. This is why I personally think that calling it "ACE" might be somewhat confusing to people who are very knowledgable about physics. Instead, something like "accumulated cyclone quality"/"ACQ" or "cyclone quality conversion factor"/"CQCF" would be more appropriate, at least imho.

Is there a physical quantity about a tropical cyclone that ACE is trying to measure? It seems to me that ACE is trying to approximate the integral of 1/T_synoptic*v_max^2dt over a storm’s lifespan, where T_synoptic is the duration between synoptic points and v_max is the maximum sustained wind speed of the storm. I have trouble seeing what physical quantity this is and why it is necessary to divide out T_synoptic.

If this measures the “quality” of a cyclone, my biggest question is why it is defined as so. Why is ACE not Σv_max? Why is ACE not Σv_max^3? What is so special about Σv_max^2? I know v^2 appears in the expression for kinetic energy, but ACE approximates 2/(m*T_synoptic)∫v_max^2dt.

While writing this post, I realized that, in a sense ∫Kdt is a useful quantity. You can in principle define a Lagrangian L = K - U (kinetic energy minus potential energy) and compute the action S = ∫Ldt, and action is a useful physical quantity; the kinetic energy of a cyclone, as shown in the original post, is given by K = 1/2∭ρ*v_max^2dV, and if gravity is assumed to be the only force acting on a tropical cyclone(i.e. assuming zero friction or drag), the potential energy of a tropical cyclone is given by U = ∭ρ*g*ydV. Since it is always possible to pick a value of y so that U = 0, it is always possible to pick a value of y such that L = K, and so ∫Kdt really would be the action of the tropical cyclone over its lifetime. I wonder if this is what ACE is trying very crudely to approximate.

ACE is a rather new form of measuring aspects of hurricanes, being developed and refined around the late 90s. It was the result of scientists scratching their heads, trying to figure out a "good" way of measuring a given hurricane's quality. Two things came into mind: strength and duration. A hurricane of "high quality" would be one that maintains very high winds and also lasts for days. Also worth noting that ACE doesn't have a specific defined "unit"; we just refer to ACE with *insert some number* ACE units.

I suppose the vmax squared is used because cubing would result in a much greater number, so I think the scientists who created the equation thought squaring would yield a reasonable number that would generally not be too small and not too large to document and keep track of. I will say, very interesting analysis on the nitty gritty physics behind ACE, and I think you're right and onto something here. As someone who was a biology major and also happened to take only a handful of physics and meteorology courses in college, that was definitely an interesting read.