## Smooth Move

My twelve year old daughter is working a science fair project on electricity and home usage. As part of her project, we have been taking lots of measurements of the electricity usage throughout our house. This provided a great opportunity to talk about smoothing and for me to publicly work through my resultant confusion. Smoothing is necessary because noise is so ubiquitous. Even if you could remove all the noise from an input device, you’ll still have a certain degree of uncertainty because the world is not fundamentally deterministic.1 Even more, smoothing is such a general problem that it traverses nearly all aspects of signal processing.

Filters are the general tool that allow engineers to work with uncertainty.2 In general, a filter is device or process that removes unwanted components or features from a signal. I like to think of a filter as a tool that takes a series of observations, and attempts to find the most likely signal that generated them. They are then a necessary tool in a noisy world. All sensors require filters, and filters play an essential (yet somehow hidden) role in our lives. [Alan Zucconi] had a great blog post on this that I leverage for the content below.

The ability to recover a signal that has been corrupted by noise depends on the type of noise and the relative proportion of noise and signal (often called the SNR or signal to noise ratio). One of the most common problems is to remove additive noise, uniformly distributed also often called Gaussian white noise. Here the noise is totally independent from the original signal. Additive uniform noise is often the result of an external interference.

There are many types of filters defined by what assumptions they make about the signal. Most all filters deal in the frequency domain, while some filters in the field of image processing do not. Some examples of filters include linear or non-linear, time-invariant or time-variant, causal or not-causal3, analog or digital, discrete-time (sampled) or continuous-time. Linear filters fall several broad categories based on what frequencies are allowed to pass. The filter passes the passband and rejects the stopband. Filters are divided into these categories and you will hear these terms used frequently in the electrical engineering community:

Low-pass filter – low frequencies are passed, high frequencies are attenuated.
High-pass filter – high frequencies are passed, low frequencies are attenuated.
Band-pass filter – only frequencies in a frequency band are passed.
Band-stop filter or band-reject filter – only frequencies in a frequency band are attenuated.
Notch filter – rejects just one specific frequency – an extreme band-stop filter.
Comb filter – has multiple regularly spaced narrow passbands giving the bandform the appearance of a comb.
All-pass filter – all frequencies are passed, but the phase of the output is modified.

The following picture helps make sense of these terms:

# Moving Average

One of the most simple filters is the ability attenuate additive noise is called the moving average filter. A Moving average is based on the assumption that independent noise is not going to change the underlying structure of the signal, so averaging a few points should attenuate the contribution of the noise. The moving average calculates the average of its neighboring points for each point in a signal. For example, from three points the filtered signal is given by averaging:

$$F_i = \frac{N_{i-1}+N_{i}+N_{i+1}}{3}$$

If all the observations are available, we can define moving average with window size $N=2k+1$ as:

$$F_i = \frac{1}{N} \sum_{j = -k}^{+k} S_{i-j}$$

While the moving average technique works well for continuous signals, it is likely to alter the original signal more than the noise itself if there are large discontinuities. Moving average is the optimal solution with linear signals which are affected by additive uniform noise.

# Centered Moving Average

A moving average introduces a constraint over $N$: it has to be an odd number. This is because a moving average requires an equal number of points $k$ before and after the center point: $N_i$. Since we count $N_i$ itself, we have $2k+1$ points, which is always odd. If we want to use moving average with an even number of points ($M = 2k$), we have two possibilities. For example, if $k=2$ and $MA$ is the moving average:

$$MA^L_4=\frac{N_{i-2} + N_{i-1} + N_{i}+ N_{i+1} }{4}$$
$$MA^R_4=\frac{N_{i-1} + N_{i} + N_{i+1}+ N_{i+2} }{4}$$

Both these expressions are valid, and there is no reason to prefer one over the other. For this reason, we can average the together to get a centered moving average. This is often referred as $2\times 4 MA$.

$$2\times 4 MA=\frac{1}{2} \left[ \frac{1}{4}\left(N_{i-2} + N_{i-1} + N_{i} + N_{i+1} \right)+ \frac{1}{4}\left( N_{i-1} + N_{i} + N_{i+1} + N_{i+2} \right) \right]=$$

$$=\frac{N_{i-2}}{8} + \frac{N_{i-1}}{4} + \frac{N_{i}}{4}+\frac{N_{i+1}}{4}+\frac{N_{i+2}}{8}$$

This is very similar to a moving average centered on $N_i$, but it helps pave the way for the next concept.

# Weighted Moving Average

Moving average treats each point in the window with the same importance. A weighted moving average values points further away from the signal, $S_i$, less by introducing a weight $W_j$ for each time step in the window:

$$F_i = \sum_{j = -k}^{+k} S_{i-j} W_{k+j}$$

with the additional constraint that all $W_j$ must sum up to $1$. Looking back at the repeated average, we can now say that $2\times 4 MA$ is equal to a weighted moving average with weights $\frac{1}{8},\frac{1}{4},\frac{1}{4},\frac{1}{2}$.

The weighted moving average is more powerful, but at the cost of more complexity. It is actually just the beginning of more complex smoothing operations, such as the convolution operator.4

# Convolution

At its most basic, convolution is a weighted average with one function constituting the weights and another the function to be averaged. I’ve used convolutions in aerodynamics, digital signal processing and applied probability. It comes up everywhere. Technically, it takes two functions and produces the integral of the pointwise multiplication of the two functions as a function of the amount that one of the original functions is translated. While convolutions are a very powerful operation, we are interested in the ability for convolutions to be a “weighted sum of echoes” or “weighted sum of memories”. They accomplish this by smearing/smoothing one signal by another or they reverse, shift, multiply and sum two inputs. To understand this better, consider two inputs:

DATA: quantities certainly corrupted by some noise – and at random positions (e.g. time or space)
PATTERN: some knowledge of how information should look like

From these, the convolution of DATA with (the mirror symmetric of the) PATTERN is another quantity that evaluates how likely it is that it is at each of the positions within the DATA.

Convolution provides a way of multiplying together’ two arrays of numbers, generally of different sizes, but of the same dimensionality, to produce a third array of numbers of the same dimensionality. In this sense, convolution is similar to cross-correlation, and measures the log-likelihood under some general assumptions (independent Gaussian noise). In general, most noise sources are very random and approximated by a normally distribution, so the PATTERN often used is the Gaussian kernel.

There are some great explanations of the intuitive meaning of convolutions on quora and stack overflow. I loved this interactive visualization. There is a great example using convolution with python code at matthew-brett.github.io.

For me, it always helps to work a real example. If a 2-D, an isotropic (i.e. circularly symmetric) Gaussian has the form:

$$G(x,y)={\frac {1}{\sigma^2 {2\pi}}}e^{-\frac{x^2+y^2}{2\,\sigma^2}}$$

For Gaussian smoothing, we use this 2-D distribution as a ‘point-spread’ function and convolution. This is often done to smooth images. Since the image is stored as a collection of discrete pixels we need to produce a discrete approximation to the Gaussian function before we can perform the convolution. In theory, the Gaussian distribution is non-zero everywhere, which would require an infinitely large convolution kernel, but in practice it is effectively zero more than about three standard deviations from the mean, so we can work with some reasonably sized kernels without losing much information. In order to perform the discrete convolution, we build a discrete approximation with $\sigma=1.0$.

$$\frac{1}{273}\, \begin{bmatrix} 1 & 4 & 7 & 4 & 1 \\ 4 & 16 & 26 & 16 & 4 \\ 7 & 26 & 41 & 26 & 7 \\ 4 & 16 & 26 & 16 & 4 \\ 1 & 4 & 7 & 4 & 1 \\ \end{bmatrix}$$

The Gaussian smoothing can be performed using standard convolution methods. The convolution can in fact be performed fairly quickly since the equation for the 2-D isotropic Gaussian shown above is separable into x and y components. Thus the 2-D convolution can be performed by first convolving with a 1-D Gaussian in the $x$ direction, and then convolving with another 1-D Gaussian in the $y$ direction.5

The effect of Gaussian smoothing on an image is to blur an image similar to a mean filter. The higher the standard deviation of the Gaussian, the more blurry a picture will look. The Gaussian outputs a weighted average of each pixel’s neighborhood, with the average weighted more towards the value of the central pixels. This is in contrast to the mean filter’s uniformly weighted average and what provides more subtle smoothing and edge-preservation by convolution when compared with a mean filter. Here is the result of a 5px gaussian filter on my picture:

One of the principle justifications for using the Gaussian as a smoothing filter is due to its frequency response. In this sense, most convolution-based smoothing filters act as lowpass frequency filters. This means that their effect is to remove high spatial frequency components from an image. The frequency response of a convolution filter, i.e. its effect on different spatial frequencies, can be seen by taking the Fourier transform of the filter. Which brings us to . . .

# The Fast Fourier Transform

The Fourier transform brings a signal into the frequency domain where it is possible to reduce the high frequency components of a signal. Because it operates in the frequency domain, Fourier analysis smoothes data using a sum of weighted sine and cosine terms of increasing frequency. The data must be equispaced and discrete smoothed data points are returned. While considered a very good smoothing procedure, fourier analysis only works when the number of points is a power of 2 or you’ve padded the data with zeros. Other advantages are the ability for a user to choose cutoff and it can be efficient since only the coefficients needed to be stored store the coefficients rather than the data points. Essentially, you rebuild the signal by creating a new one by adding trigonometric functions.

When the Fourier transform is computed practically, the Fast Fourier Transform (FFT) is used. First, no one wants an approximation built by infinite sums of frequencies, so we use a discrete Fourier transform (DFT). The FFT works by factorizing the DFT matrix into a product of sparse (mostly zero) factors. Due to the huge applications of FFTs, this has been a very active area of research. Importantly, modern techniques to compute the FFT operate at $O(n \log{n})$, compared with the naïve transform of N points in the naive way that would take $O(N^2)$ arithmetical operations.

In practice an analyst will take a FFT followed by reduction of amplitudes of high frequencies, followed by IFFT (inverse FFT).

A little bit of python (helped by numpy) can show how this in action:

x = np.arange(40)
y = np.log(x + 1) * np.exp(-x/8.) * x**2 + np.random.random(40) * 15
rft = np.fft.rfft(y)
rft[5:] = 0   # Note, rft.shape = 21
y_smooth = np.fft.irfft(rft)

plt.plot(x, y, label='Original')
plt.plot(x, y_smooth, label='Smoothed')
plt.legend(loc=0).draggable()
plt.show()
`

# Savitzky-Golay filter

Remember the Chuck Wagon burger in school that incorporated a little bit of every food from the week before in it?

The Savitzky–Golay filter uses nearly everything we have talked about above. It first convolves data by fitting successive sub-sets of adjacent data points with a low-degree polynomial by the method of linear least squares.

Because python gives you a set of tools that work out of the box, I went ahead and used this one to give to my daughter for her science fair. You can see my code below, but it generated this plot showing electricity usage in our house over 10 days smoothed by Savitzky-Golay windows length 51, and 6th order polynomial.

# Kálmán filter

Ok, if you have survived this far, I’ve saved the best for last. I’ve used Kalman filters more than any other tool and they really combine everything. Just this last July, R. E. Kálmán passed away. At the heart of the Kalman filter is an algorithm that uses a series of measurements observed over time, containing statistical noise and other inaccuracies to produces estimates of unknown variables. The Kalman filter ‘learns’ by using Bayesian inference and estimating a joint probability distribution over the variables for each timeframe.

My background with the Kalman filter comes from its applications in guidance, navigation, and control of vehicles, particularly aircraft and spacecraft. The most famous early use of the Kalman filter was in the Apollo navigation computer that took Neil Armstrong to the moon and back.

The Kalman filter permits exact inference in a linear dynamical system, which is a Bayesian model similar to a hidden Markov model where the state space of the latent variables is continuous and where all latent and observed variables have a Gaussian distribution.

Computing estimates with the Kalman filter is a two-step process: a prediction and update. In the prediction step, the Kalman filter produces estimates of current state variables and their uncertainties. Once the outcome of the next measurement (necessarily corrupted with some amount of error, including random noise) is observed, these estimates are updated using a weighted average, with more weight being given to estimates with higher certainty. The algorithm is recursive and can run in real time, using only input measurements and the previously calculated state and its uncertainty matrix; no additional past information is required.

I would write more about it here, but this article by Ramsey Faragher is better than anything I could produce to give an intuitive view of the Kalman filter. This article “How a Kalman filter works in Pictures” is also incredible.

According to Greg Czerniak Kalman filters can help when four conditions are true:
1. You can get measurements of a situation at a constant rate.
2. The measurements have error that follows a bell curve.
3. You know the mathematics behind the situation.
4. You want an estimate of what’s really happening.

He provides an example showing the ability for a Kalman filter to remove noise from a voltage signal:

You can find his code here.

# Usage

In general, if you want to use a serious filter, I like the Savitzky-Golay and Kalman filter. The Savitzky-Golay is best for smoothing data. The idea behind the Savitzky-Golay smoothing filter is to find a filter that preserves higher-order moments while smoothing the data. It reduces noise while maintaining the shape and height of peaks. Unless you have special circumstances that you want to overcome, use Savitzky-Golay. Of course the Kalman filter could do this. However it is a tool with massive scope. You can pull signals out of impossible noisescapes with Kalman, but it takes a lot of expertise to grasp when it’s appropriate, and how best to implement it.

In some cases, the moving average, or weighted moving average, is just fine, but it bulldozes over the finer structure.

# References

I’m so not an expert on filters. If anything above is (1) wrong or (2) needs more detail, see these references:

• E. Davies Machine Vision: Theory, Algorithms and Practicalities, Academic Press, 1990, pp 42 – 44.
• R. Gonzalez and R. Woods Digital Image Processing, Addison-Wesley Publishing Company, 1992, p 191.
• R. Haralick and L. Shapiro Computer and Robot Vision, Addison-Wesley Publishing Company, 1992, Vol. 1, Chap. 7.
• B. Horn Robot Vision, MIT Press, 1986, Chap. 8.
• D. Vernon Machine Vision, Prentice-Hall, 1991, pp 59 – 61, 214.
• Whittaker, E.T; Robinson, G (1924). The Calculus Of Observations. Blackie & Son. pp. 291–6. OCLC 1187948.. “Graduation Formulae obtained by fitting a Polynomial.”
• Guest, P.G. (2012) [1961]. “Ch. 7: Estimation of Polynomial Coefficients”. Numerical Methods of Curve Fitting. Cambridge University Press. pp. 147–. ISBN 978-1-107-64695-7.
• Savitzky, A.; Golay, M.J.E. (1964). “Smoothing and Differentiation of Data by Simplified Least Squares Procedures”. Analytical Chemistry. 36 (8): 1627–39.
• Savitzky, Abraham (1989). “A Historic Collaboration”. Analytical Chemistry. 61 (15): 921A–3A.

# Code

I generally write these posts to share my code:

# Footnotes

1. For friends who have studied physics: Schrödinger’s equation induces a unitary time evolution, and it is deterministic, but indeterminism in Quantum Mechanics is given by another “evolution” that the wavefunction may experience: wavefunction collapse. This is the source of indeterminism in Quantum Mechanics, and is a mechanism that is still not well understood at a fundamental level. For a real treatment of this, check out Decoherence and the Appearance of a Classical World in Quantum Theory
2. Math presents a very different understanding of filters when compared to signal processing where a filter is in general a special subset of a partially ordered set. They appear in order and lattice theory, but can also be found in topology whence they originate. The dual notion of a filter is an ideal
3. A filter is non-causal if its present output depends on future input. Filters processing time-domain signals in real time must be causal, but not filters acting on spatial domain signals or deferred-time processing of time-domain signals.
4. See Functional Analysis for more details on how to show equivalence.
5. The Gaussian is in fact the only completely circularly symmetric operator which can be decomposed like this.

## Three Way Troubleshooting

Tonight, I was rewiring switches to a more modern set of switches. These days I don’t have time to learn by experience, I have to think my way through this. Without experience, I have to go back to first principles. Funny enough, understanding a four way switch is very similar to understanding digital logic and computation in general.

A three way switch is an electrical component that lets you turn a light on or off from three or more locations. Any one toggle should change the state of the light. To control a light from one location, all you need is a simple on/off switch. The switch either closes the circuit, in which case the light goes on, or it opens the circuit, in which case the light goes off. Essentially, the switch takes two ends of a wire and connects or disconnects them. This is different than a one-switch circuit where the position of the switch correlates with the state of the light. In the examples below, up will mean on, and down will mean off.

First, there are $2^n$ states for $n$ switches. A 4-way switch has three lights or eight states. Mine were wrong. Lauren (my 12 year old) and I measured three switches: 1,2 and 3. Switch 2 was the four-way switch. Our measurements produced:

Case 1 2 3 Light Ideal
1 0 0 0 off off
2 0 0 1 off on
3 0 1 1 off off
4 0 1 0 on on
5 1 1 0 off off
6 1 1 1 on on
7 1 0 1 off off
8 1 0 0 off on

Two states are off: cases two and eight. They should be closed, but are open.

The next piece was to understand how the circuit actually works so I could look at what configuration might be causing the current state machine. This simulation (credit to falstad.com) was awesome.

The key insight was that both failing states should have counted on the four way to close the circuit but the circuit was staying open. With that knowledge, I was able to put the four-way together per the diagram below.

And, for my switches in particular:

## Weaponizing the Weather

“Intervention in atmospheric and climatic matters . . . will unfold on a scale difficult to imagine at present. . . . this will merge each nation’s affairs with those of every other, more thoroughly than the threat of a nuclear or any other war would have done.” — J. von Neumann

Disclaimer: This is just me exploring a topic that I’m generally clueless on, explicitly because I’m clueless on it. My views and the research discussed here has nothing to do with my work for the DoD.

# Why do we care?

Attempting to control the weather is older than science itself. While it is common today to perform cloud seeding to increase rain or snow, weather modification has the potential to prevent damaging weather from occurring; or to provoke damaging weather as a tactic of military or economic warfare. This scares all of us, including the UN who banned weather modification for the purposes of warfare in response to US actions in Vietnam to induce rain and extend the East Asian monsoon season (see operation popeye). Unfortunately, this hasn’t stopped Russia and China from pursuing active weather modification programs with China generally regarded as the largest and most active. While Russia is famous for sophisticated cloud-seeding in 1986 to prevent radioactive rain from the Chernobyl reactor accident from reaching Moscow, see China Leads the Weather Control Race and China plans to halt rain for Olympics to understand the extent of China’s efforts in this area.

The Chinese have been tinkering with the weather since the late 1950s, trying to bring rains to the desert terrain of the northern provinces. Their bureau of weather modification was established in the 1980s and is now believed to be the largest in the world. It has a reserve army of 37,000 people, which might sound like a lot, until we consider the scale of an average storm. The numbers that describe weather are big. At any instant there are approximately 2,000 thunderstorms and every day there are 45,000 thunderstorms, which contain some combination of heavy rain, hail, microbursts, wind shear, and lightning. The energy involved is staggering: a tropical storm can have an energy equal to 10,000 one-megaton hydrogen bombs. A single cloud contains about a million pounds of water so a mid-size storm would contain about 3 billion pounds of water. If anyone ever figures out how to control all this mass and energy they would make an excellent bond villain.

The US government has conducted research in weather modification as well. In 1970, then ARPA Director Stephen J. Lukasik told the Senate Appropriations Committee: “Since it now appears highly probable that major world powers have the ability to create modifications of climate that might be seriously detrimental to the security of this country, Nile Blue [a computer simulation] was established in FY 70 to achieve a US capability to (1) evaluate all consequences of of a variety of possible actions … (2) detect trends in in the global circulation which foretell changes … and (3) determine if possible , means to counter potentially deleterious climatic changes … What this means is learning how much you have to tickle the atmosphere to perturb the earth’s climate.” Sounds like a reasonable program for the time.

Military applications are easy to think up. If you could create a localized could layer, you could decrease performance of ground and airborne IRSTs particularly in the long-wave. (Cloud mean-diameter is typically 10 to 15 microns.) You could send hurricanes toward your adversary or increase the impact of an all weather advantage. (Sweet.) You could also do more subtle effects such as inuring the atmosphere towards your communications technology or degrade the environment to a state less optimal for an adversary’s communications or sensors. Another key advantage would be to make the environment unpredictable. Future ground-based sensing and fusing architectures such as multi-static and passive radars rely on a correctly characterized environment that could be impacted by both intense and unpredictable weather.

Aside from military uses, climate change (both perception and fact) may drive some nations to seek engineered solutions. Commercial interests would welcome the chance to make money cleaning up the mess they made money making. And how are we going to sort out and regulate that without options and deep understanding? Many of these proposals could have dual civilian and military purposes as they originate in Cold War technologies. As the science advances, will we be able to prevent their renewed use as weapons? Could the future hold climatological conflicts, just as we’ve seen cyber warfare used to presage invasion as recently seen between Ukraine and Russia? If so, climate influence would be a way for a large state to exert an influence on smaller states.

Considering all of this, it would be prudent to have a national security policy that accounts for weather modification and manipulation. Solar radiation management, called albedo modification, is considered to be a potential option for addressing climate change and one that may get increased attention. There are many research opportunities that would allow the scientific community to learn more about the risks and benefits of albedo modification, knowledge which could better inform societal decisions without imposing the risks associated with large-scale deployment. According to Carbon Dioxide Removal and Reliable Sequestration (2015) by the National Academy of Sciences, there are several hypothetical, but plausible, scenarios under which this information would be useful. They claim (quoting them verbatim):

1. If, despite mitigation and adaptation, the impacts of climate change still become intolerable (e.g., massive crop failures throughout the tropics), society would face very tough choices regarding whether and how to deploy albedo modification until such time as mitigation, carbon dioxide removal, and adaptation actions could significantly reduce the impacts of climate change.
2. The international community might consider a gradual phase-in of albedo modification to a level expected to create a detectable modification of Earth’s climate, as a large-scale field trial aimed at gaining experience with albedo modification in case it needs to be scaled up in response to a climate emergency. This might be considered as part of a portfolio of actions to reduce the risks of climate change.
3. If an unsanctioned act of albedo modification were to occur, scientific research would be needed to understand how best to detect and quantify the act and its consequences and impacts.

# What has been done in the past?

Weather modification was limited to magic and prayers until the 18th century when hail cannons were fired into the air to break up storms. There is still an industrial base today if you would like to have your own hail cannon. Just don’t move in next door if you plan on practicing.

Despite their use on a large scale, there is no evidence in favor of the effectiveness of these devices. A 2006 review by Jon Wieringa and Iwan Holleman in the journal Meteorologische Zeitschrift summarized a variety of negative and inconclusive scientific measurements, concluding that “the use of cannons or explosive rockets is waste of money and effort”. In the 1950s to 1960s, Wilhelm Reich performed cloudbusting experiments, the results of which are controversial and not widely accepted by mainstream science.

However, during the cold war the US government committed to a ambitious experimental program named Project Stormfury for nearly 20 years (1962 to 1983). The DoD and NOAA attempted to weaken tropical cyclones by flying aircraft into them and seeding them with silver iodide. The proposed modification technique involved artificial stimulation of convection outside the eye wall through seeding with silver iodide. The artificially invigorated convection, it was argued, would compete with the convection in the original eye wall, lead to reformation of the eye wall at larger radius, and thus produce a decrease in the maximum wind. Since a hurricane’s destructive potential increases rapidly as its maximum wind becomes stronger, a reduction as small as 10{aaa01f1184b23bc5204459599a780c2efd1a71f819cd2b338cab4b7a2f8e97d4} would have been worthwhile. Modification was attempted in four hurricanes on eight different days. On four of these days, the winds decreased by between 10 and 30{aaa01f1184b23bc5204459599a780c2efd1a71f819cd2b338cab4b7a2f8e97d4}. The lack of response on the other days was interpreted to be the result of faulty execution of the experiment or poorly selected subjects.

These promising results have, however, come into question because recent observations of unmodified hurricanes indicate: I) that cloud seeding has little prospect of success because hurricanes contain too much natural ice and too little super cooled water, and 2) that the positive results inferred from the seeding experiments in the 1960s probably stemmed from inability to discriminate between the expected effect of human intervention and the natural behavior of hurricanes. The legacy of this program is the large global infrastructure today that routinely flies to inject silver iodide to cause localized rain with over 40 countries actively seeding clouds to control rainfall. Unfortunately, we are still pretty much helpless in the face of a large hurricane.

That doesn’t mean the Chinese aren’t trying. In 2008, China assigned 30 airplanes, 4,000 rocket launchers, and 7,000 anti-aircraft guns in an attempt to stop rain from disrupting the 2008 Olympics by shooting various chemicals into the air at any threatening clouds in the hopes of shrinking rain drops before they reached the stadium. Due to the difficulty of conducting controlled experiments at this scale, there is no way to know if this was effective. (Yes, this is the country that routinely bulldozes entire mountain ranges to make economic regions.)

But the Chinese aren’t the only ones. In January, 2011, several newspapers and magazines, including the UK’s Sunday Times and Arabian Business, reported that scientists backed by Abu Dhabi had created over 50 artificial rainstorms between July and August 2010 near Al Ain. The artificial rainstorms were said to have sometimes caused hail, gales and thunderstorms, baffling local residents. The scientists reportedly used ionizers to create the rainstorms, and although the results are disputed, the large number of times it is recorded to have rained right after the ionizers were switched on during a usually dry season is encouraging to those who support the experiment.

While we would have to understand the technology very well first and have a good risk mitigation strategy, I think there are several promising technical areas that merit further research.

# What are the technical approaches?

So while past experiments are hard to learn much from and far from providing the buttons to control the weather, there are some promising technologies I’m going to be watching. There are five different technical approaches I was able to find:

1. Altering the available solar energy by introducing materials to absorb or reflect sunshine
2. Adding heat to the atmosphere by artificial means from the surface
3. Altering air motion by artificial means
4. Influencing the humidity by increasing or retarding evaporation
5. Changing the processes by which clouds form and causing precipitation by using chemicals or inserting additional water into the clouds

In these five areas, I see several technical applications that are both interesting and have some degree of potential utility.

## Modeling

Below is the 23-year accuracy of the U.S. GFS, the European ECMWF, the U.K. Government’s UKMET, and a model called CDAS which has never been modified, to serve as a “constant.” As you would expect, model accuracy is gradually increasing (1.0 is 100{aaa01f1184b23bc5204459599a780c2efd1a71f819cd2b338cab4b7a2f8e97d4} accurate). Weather models are limited by computation and the scale of input data: for a fixed amount of computing power, the smaller the grid (and more accurate the prediction), the smaller time horizon for predictions. As more sensors are added and fused together, accuracy will keep improving.

Weather requires satellite and radar imagery that are truly on the very small scale. Current accuracy is an effective observation spacing of around 5 km. Radar data are only available to a fairly short distance from the coast. Satellite wind measurements can only resolve detail on about a 25 km scale. Over land, data from radar can be used to help predict small scale and short lived detail.

Modeling is important, because understanding is necessary for control. With increased accuracy, we can understand weather’s leverage points and feedback loops. This knowledge is important, because increased understanding would enable applying the least amount of energy where it matters most. Interacting with weather on a macro scale is both cost prohibitive and extremely complex.

## Ionospheric Augmentation

Over the horizon radars (commonly called OTHR) have the potential to see targets hundreds of miles away because they aren’t limited by their line of sight like conventional microwave radars. They accomplish this by bouncing off the horizon, but this requires a sufficiently dense ionosphere that isn’t always there. Since the ionosphere is ionized by solar radiation, the solar radiation is stronger when the earth is more tilted towards the sun in the summer. To compensate for this, artificial ionospheric mirrors could bounce HF signals more consistently and precisely over broader frequencies. Tests have shown that these mirrors could theoretically reflect radio waves with frequencies up to 2 GHz, which is nearly two orders of magnitude higher than waves reflected by the natural ionosphere. This could have significant military applications such as low frequency (LF) communications, HF ducted communications, and increased OTHR performance.

This concept has been described in detail by Paul A. Kossey, et al. in a paper entitled “Artificial Ionospheric Mirrors.” The authors describe how one could precisely control the location and height of the region of artificially produced ionization using crossed microwave beams, which produce atmospheric breakdown. The implications of such control are enormous: one would no longer be subject to the vagaries of the natural ionosphere but would instead have direct control of the propagation environment. Ideally, these artificial mirrors could be rapidly created and then would be maintained only for a brief operational period.

## Local Introduction of Clouds

There are several methods for seeding clouds. The best-known dissipation technique for cold fog is to seed it from the air with agents that promote the growth of ice crystals. They include dropping pyrotechnics on lop of existing clouds. penetrating clouds, with pyrotechnics and liquid generators, shooting rockets into clouds, and working from ground-based generators. Silver iodide is frequently used lo cause precipitation, and effects usually are seen in about thirty minutes. Limited success has been noted in fog dispersal and improving local visibility through introduction of hygroscopic substances.

However, all of these techniques seem like a very inexact science and 30 minutes remains far from the timescales needed for clouds on demand. From my brief look at it, we are just poking around in cloud formation. For the local introduction of clouds to be useful in military applications, there have to be a suite of techniques robust to changing weather. More research in this area might be able to effect chain reactions to cause massive cloud formations. Real research in this area could help it emerge from pseudo-science. There is a lot of it in this area. This Atlantic article titled Dr. Wilhelm Reich’s Orgasm-Powered Cloudbuster is pretty amusing and pretty indicative of the genre.

## Fog Removal

Ok, so no-one can make clouds appear on demand in a wide range of environments, but is technology better when it comes to removing fog? The best-known dissipation technique is heating because a small temperature increase is usually sufficient to evaporate fog. Since heating over a very wide scale usually isn’t practical, the next most effective technique is hygroscopic seeding. Hygroscopic seeding uses agents that absorb water vapor. This technique is most effective when accomplished from the air but can also be accomplished from the ground. Optimal results require advance information on fog depth, liquid water content, and wind.

In the 20th century several methods have been proposed to dissipate fog. One of them is to burn fuel along the runway, heat the fog layer and evaporate droplets. It has been used in Great Britain during World War II to allow British bombers returning from Germany to land safely in fog conditions. Helicopters can dissipate fog by flying slowly across the top surface and mix warm dry air into the fog. The downwash action of the rotors forces air from above into the fog, where it mixes, producing lower humidity and causing the fog droplets to evaporate. Tests were carried out in Florida and Virginia, and in both places cleared areas were produced in the helicopter wakes. Seeding with polyelectrolytes causes electric charges to develop on drops and has been shown to cause drops to coalesce and fallout. Other techniques that have been tried include the use of high-frequency (ultrasonic) vibrations, heating with laser rays and seeding with carbon black to alter the radiative properties1.

However, experiments have confirmed that large-scale fog removal would require exceeding the power density exposure limit of $100 \frac{\text{watt}}{m^2}$ and would be very expensive. Field experiments with lasers have demonstrated the capability to dissipate warm fog at an airfield with zero visibility. This doesn’t mean that capability on a smaller scale isn’t possible. Generating $1 \frac{\text{watt}}{cm^2}$, which is approximately the US large power density exposure limit, raised visibility to one quarter of a mile in 20 seconds. Most efforts have been made on attempts to increase the runway visibility range on airports, since airline companies face millions of dollars loss every year due to fog appearance on the runway. This thesis examines in the issue in depth.

# Emerging Enabling Technologies

In looking at this topic, I was able to find several interesting technologies that may develop and make big contributions to weather research.

## Carbon Dust

Just as a black tar roof easily absorbs solar energy and subsequently radiates heat during a sunny day, carbon black also readily absorbs solar energy. When dispersed in microscopic form in the air over a large body of water, the carbon becomes hot and heats the surrounding air, thereby increasing the amount of evaporation from the water below. As the surrounding air heats up, parcels of air will rise and the water vapor contained in the rising air parcel will eventually condense to form clouds. Over time the cloud droplets increase in size as more and more water vapor condenses, and eventually they become too large and heavy to stay suspended and will fall as rain. This technology has the potential to trigger localized flooding and bog down troops and their equipment.

## Nanotech

Want to think outside the box? Smart materials based on nanotechnology are currently being developed with processing capability. They could adjust their size to optimal dimensions for a given fog seeding situation and even make continual adjustments. They might also enhance their dispersal qualities by adjusting their buoyancy, by communicating with each other, and by steering themselves within the fog. If successful, they will be able to provide immediate and continuous effectiveness feedback by integrating with a larger sensor network and could also change their temperature and polarity to improve their seeding effects.

If we combine this with high fidelity models, things can get very interesting. If we can model and understand the leverage points of a weather system, nano-clouds may be able to have an dramatic effect. Nanotechnology also offers possibilities for creating simulated weather. A cloud, or several clouds, of microscopic computer particles, all communicating with each other and with a larger control system could mimic the signatures of specific weather patterns if tailored to the parameters of weather models.

## High power lasers

The development of directed radiant energy technologies, such as microwaves and lasers, could provide new possibilities. Everyone should hate firing rockets and chemicals into the atmosphere. The advent of ultrashort laser pulses and the discovery of self-guided ionized filaments (see Braun et al., 1985) might provide the opportunity. Jean-Pierre Wolf has used using ultrashort laser pulses to create lightning and cue cloud formation. Prof Wolf says, “We did it on a laboratory scale, we can already create clouds, but not on a macroscopic scale, so you don’t see a big cloud coming out because the laser is not powerful enough and because of a lot of technical parameters that we can’t yet control,” from this cnn article.

# What now?

So we have all the elements of scientific discipline and could use a national strategy in this area that includes the ethics, policy, technology and military employment doctrine. The military and civilian community already invests heavily in sensors and modeling of weather effects. These should be coupled with feasible excitation mechanisms to create a tight innovation loop. Again, this area is sensitive and politically charged, but there is a clear need to pull together sensors, processing capability and excitation mechanisms to ensure we have the right responses and capabilities. With such a dubious and inconclusive past, is there a potential future for weather modification? I think we have a responsibility for pursing knowledge even in areas where the ethical boundaries are not well established. Ignorance is never a good strategy. Just because we might open Pandora’s box, doesn’t mean that a less morally responsible nation or group won’t get there first. We can always abstain from learning a new technology, but if we are caught by surprise, we won’t have the knowledge to develop a good counter-strategy.

# References

1. http://csat.au.af.mil/2025/volume3/vol3ch15.pdf
2. http://www.wired.com/2009/12/military-science-hack-stormy-skies-to-lord-over-lightning/
3. PROSPECTS FOR WEATHER MODIFICATION

1. DUMBAI, MA, et al. “ORGANIC HEAT-TRANSFER AGENTS IN CHEMICAL-INDUSTRY.” KHIMICHESKAYA PROMYSHLENNOST 1 (1990): 10-15.

## What was the most Geeky Event in History?

While I can’t get into the background here, I was recently asked to describe the most geeky event in history. Something like this is hard to bound and as I asked those around me I got lots of answers from moment the zero was invented (“without that, you got nothing”) to the first demo of the transistor (pretty good one) to the Trinity Test for the Manhattan Project. All of these were interesting, but “Geeky” implies not necessarily profound, but technical, funny, entertaining and weird. As I tried to put together my answers, I came up with the following goals:

• geeky stuff is funny, so the moment should at least make you smile
• geeky stuff is esoteric and should surprise and be a little weird to the general public
• geeky stuff is technical; a geeky moment should be the culmination of a long technical slog and unveil a new tech in a novel way
• geeky stuff is changing the world, so this moment should have at least a brush with history

So, I came up with four events: (1) A profound historical event, (2) A funny event, (3) a profound economic event, and (4) an tech awe-inspiring event.

## The Profound Event

On 9 December 1932, 27 year old Marian Rejewski (a Polish mathematician) was given some German manuals and monthly keys for their Enigma. On top of his recently developed theory of permutations and groups, this enabled him to work out the Enigma scrambler wiring after he had the insight that the Nazi keyboard was wired to the entry drum, not in keyboard order, but in alphabetical order. He describes what happened next: “The very first trial yielded a positive result. From my pencil, as if by magic, begin to issue numbers designating the wiring”. By Christmas he was decoding nearly all German communications. Not only was this one of the greatest breakthrough cryptologic history, but it eventually resulted in the British capability listen to every conversation made between Germans. This played a big role in decimating a superior German Navy and Luftwaffe, and possibly swaying the war in favor of allies, in addition to starting the modern field of computer science.

## The Funny Event

In the fall of 1971, the twenty-year-old Wozniak was inspired by Esquire to build a “Blue Box” that enabled him to create the 2600Hz tone to control the, then analog, phone network. He took the name “Berkeley Blue” while his 17 year old business partner Steve Jobs took the call sign “Oaf Tobar.” After a visit to the original phone phreak, Captain Crunch, and a short detainment by the Police, he decided to put his blue box to good use and do something both epic and geeky: crank call the Pope. Using his blue box he managed to route his call to the Vatican. “In this heavy accent I announced that I was Henry Kissinger calling on behalf of President Nixon. I said, ‘Ve are at de summit meeting in Moscow, and we need to talk to de pope.'” The Vatican responded that the pope was sleeping but that they would send someone to wake him. Woz arranged to call back in an hour.
Woz recalls, “Well, an hour later I called back and she said, ‘Okay, we will put the bishop on, who will be the translator.’ So I told him, still in that heavy accent, ‘Dees is Mr. Kissinger.’ And he said, ‘Listen, I just spoke to Mr. Kissinger an hour ago.’ You see, they had checked out my story and had called the real Kissinger in Moscow.”
Aside from the raw audacity required to prank world leaders, there is something very geeky about building a piece of hardware out of spare parts, mastering the world-wide phone system and roping in a key source of the modern desktop, desktop publishing, digital entertainment and mobile devices in the operation.

## A Profound Geeky Economic Event

The moment when Dan Bricklin – wrote the original spreadsheet program, VisiCalc, on an Apple II. It is hard to overstate the impact spreadsheets have had on the modern economy and the PC industry . . . and it was written in assembler, which adds major geek cred.

## Tech Awe-Inspiring Event

I’ve always been in awe of Von Neumann and his impact on science and defense technology. In particular, in May 1945, he hopped on a train from Aberdeen, Maryland to Los Alamos, New Mexico. At the time, he was solving some of the hardest problems on the Manhattan project and was traveling to go provide technical advise leading up to the trinity test. He had already established game theory, numerical analysis and a good bit of quantum physics. As a side project, he had just seen a demonstration of the ENIAC computer and had been asked to write a memorandum describing the project. I’ve written a lot of memos describing government projects, but von Neumann’s 101 page hand-written “The First Draft of a Report on the EDVAC” was finished by the time he arrived in Los Alamos. He mailed it to his colleague Herman Goldstine, who typed it up, got it reviewed, and published it the next month (without any patent). His memo described the architecture of the EDVAC, the follow-on to ENIAC which was to become the world’s first von Neumann machine and was the first published description of the logical design of a computer using the stored-program concept that formed the blue-prints for 50 years of computers.